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\n  \n 2024\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n Time-fractional porous medium equation: Erdélyi–Kober integral equations, compactly supported solutions, and numerical methods.\n \n \n \n\n\n \n López, B.; Okrasińska-Płociniczak, H.; Płociniczak, Ł.; and Rocha, J.\n\n\n \n\n\n\n Communications in Nonlinear Science and Numerical Simulation, 128: 107692. 2024.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{lopez2024time,\n  title={Time-fractional porous medium equation: Erd{\\'e}lyi--Kober integral equations, compactly supported solutions, and numerical methods},\n  author={L{\\'o}pez, Belen and Okrasi{\\'n}ska-P{\\l}ociniczak, Hanna and P{\\l}ociniczak, {\\L}ukasz and Rocha, Juan},\n  journal={Communications in Nonlinear Science and Numerical Simulation},\n  volume={128},\n  pages={107692},\n  year={2024},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n Optimal strategy for trail running with nutrition and fatigue factors.\n \n \n \n\n\n \n Jaszczak, B.; and Płociniczak, Ł.\n\n\n \n\n\n\n arXiv preprint arXiv:2401.02919. 2024.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{jaszczak2024optimal,\n  title={Optimal strategy for trail running with nutrition and fatigue factors},\n  author={Jaszczak, Bogna and P{\\l}ociniczak, {\\L}ukasz},\n  journal={arXiv preprint arXiv:2401.02919},\n  year={2024}\n}\n
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\n  \n 2023\n \n \n (6)\n \n \n
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\n \n\n \n \n \n \n \n Stability of fixed points in an approximate solution of the spring-mass running model.\n \n \n \n\n\n \n Wróblewska, Z.; Kowalczyk, P.; and Płociniczak, Ł.\n\n\n \n\n\n\n IMA Journal of Applied Mathematics, 88(3): 429–454. 2023.\n \n\n\n\n
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@article{wroblewska2023stability,\n  title={Stability of fixed points in an approximate solution of the spring-mass running model},\n  author={Wr{\\'o}blewska, Zofia and Kowalczyk, Piotr and P{\\l}ociniczak, {\\L}ukasz},\n  journal={IMA Journal of Applied Mathematics},\n  volume={88},\n  number={3},\n  pages={429--454},\n  year={2023},\n  publisher={Oxford University Press}\n}\n\n
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\n \n\n \n \n \n \n \n Energy variations and periodic solutions in a switched inverted pendulum model of human running gaits.\n \n \n \n\n\n \n Kowalczyk, P.; Płociniczak, Ł.; and Wróblewska, Z.\n\n\n \n\n\n\n Physica D: Nonlinear Phenomena, 443: 133554. 2023.\n \n\n\n\n
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@article{kowalczyk2023energy,\n  title={Energy variations and periodic solutions in a switched inverted pendulum model of human running gaits},\n  author={Kowalczyk, Piotr and P{\\l}ociniczak, {\\L}ukasz and Wr{\\'o}blewska, Zofia},\n  journal={Physica D: Nonlinear Phenomena},\n  volume={443},\n  pages={133554},\n  year={2023},\n  publisher={North-Holland}\n}\n\n
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\n \n\n \n \n \n \n \n A linear Galerkin numerical method for a quasilinear subdiffusion equation.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Applied Numerical Mathematics, 185: 203–220. 2023.\n \n\n\n\n
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@article{plociniczak2023linear,\n  title={A linear Galerkin numerical method for a quasilinear subdiffusion equation},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Applied Numerical Mathematics},\n  volume={185},\n  pages={203--220},\n  year={2023},\n  publisher={North-Holland}\n}\n\n
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\n \n\n \n \n \n \n \n Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient.\n \n \n \n\n\n \n Płociniczak, Ł.; and Taźbierski, K.\n\n\n \n\n\n\n arXiv preprint arXiv:2310.04246. 2023.\n \n\n\n\n
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@article{plociniczak2023fully,\n  title={Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient},\n  author={P{\\l}ociniczak, {\\L}ukasz and Ta{\\'z}bierski, Kacper},\n  journal={arXiv preprint arXiv:2310.04246},\n  year={2023}\n}\n\n
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\n \n\n \n \n \n \n \n Convolution Quadrature for the quasilinear subdiffusion equation.\n \n \n \n\n\n \n López-Fernández, M.; and Płociniczak, Ł.\n\n\n \n\n\n\n arXiv preprint arXiv:2311.00081. 2023.\n \n\n\n\n
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@article{lopez2023convolution,\n  title={Convolution Quadrature for the quasilinear subdiffusion equation},\n  author={L{\\'o}pez-Fern{\\'a}ndez, Maria and P{\\l}ociniczak, {\\L}ukasz},\n  journal={arXiv preprint arXiv:2311.00081},\n  year={2023}\n}\n\n
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\n \n\n \n \n \n \n \n Numerical methods and regularity properties for viscosity solutions of nonlocal in space and time diffusion equations.\n \n \n \n\n\n \n del Teso, F.; and Płociniczak, Ł.\n\n\n \n\n\n\n arXiv preprint arXiv:2311.14317. 2023.\n \n\n\n\n
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@article{del2023numerical,\n  title={Numerical methods and regularity properties for viscosity solutions of nonlocal in space and time diffusion equations},\n  author={del Teso, F{\\'e}lix and P{\\l}ociniczak, {\\L}ukasz},\n  journal={arXiv preprint arXiv:2311.14317},\n  year={2023}\n}\n\n
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\n  \n 2022\n \n \n (6)\n \n \n
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\n \n\n \n \n \n \n \n Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Applied Numerical Mathematics, 179: 105–124. 2022.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2022linear,\n  title={Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Applied Numerical Mathematics},\n  volume={179},\n  pages={105--124},\n  year={2022},\n  publisher={North-Holland}\n}\n\n
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\n \n\n \n \n \n \n \n Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line.\n \n \n \n\n\n \n Okrasińska-Płociniczak, H.; and Płociniczak, Ł.\n\n\n \n\n\n\n Applied Mathematics and Computation, 424: 127033. 2022.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{okrasinska2022second,\n  title={Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line},\n  author={Okrasi{\\'n}ska-P{\\l}ociniczak, Hanna and P{\\l}ociniczak, {\\L}ukasz},\n  journal={Applied Mathematics and Computation},\n  volume={424},\n  pages={127033},\n  year={2022},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n On a discrete composition of the fractional integral and Caputo derivative.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Communications in Nonlinear Science and Numerical Simulation, 108: 106234. 2022.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2022discrete,\n  title={On a discrete composition of the fractional integral and Caputo derivative},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Communications in Nonlinear Science and Numerical Simulation},\n  volume={108},\n  pages={106234},\n  year={2022},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method.\n \n \n \n\n\n \n Płociniczak, Ł.; and Świtała, M.\n\n\n \n\n\n\n Fractional Calculus and Applied Analysis, 25(4): 1651–1687. 2022.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2022numerical,\n  title={Numerical scheme for Erd{\\'e}lyi--Kober fractional diffusion equation using Galerkin--Hermite method},\n  author={P{\\l}ociniczak, {\\L}ukasz and {\\'S}wita{\\l}a, Mateusz},\n  journal={Fractional Calculus and Applied Analysis},\n  volume={25},\n  number={4},\n  pages={1651--1687},\n  year={2022},\n  publisher={Springer International Publishing Cham}\n}\n\n
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\n \n\n \n \n \n \n \n Error of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth data.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Computers & Mathematics with Applications, 127: 181–191. 2022.\n \n\n\n\n
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@article{plociniczak2022error,\n  title={Error of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth data},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Computers \\& Mathematics with Applications},\n  volume={127},\n  pages={181--191},\n  year={2022},\n  publisher={Pergamon}\n}\n\n
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\n \n\n \n \n \n \n \n The Bushell-Okrasi$\\$'nski inequality.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n arXiv preprint arXiv:2203.15256. 2022.\n \n\n\n\n
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@article{plociniczak2022bushell,\n  title={The Bushell-Okrasi$\\backslash$'nski inequality},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={arXiv preprint arXiv:2203.15256},\n  year={2022}\n}\n\n
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\n  \n 2021\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n Oscillatory behaviour analysis of a liquid rise in cylindrical capillaries.\n \n \n \n\n\n \n Płociniczak, Ł.; and Świtała, M.\n\n\n \n\n\n\n Communications in Nonlinear Science and Numerical Simulation, 96: 105647. 2021.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2021oscillatory,\n  title={Oscillatory behaviour analysis of a liquid rise in cylindrical capillaries},\n  author={P{\\l}ociniczak, {\\L}ukasz and {\\'S}wita{\\l}a, Mateusz},\n  journal={Communications in Nonlinear Science and Numerical Simulation},\n  volume={96},\n  pages={105647},\n  year={2021},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n A linear Galerkin numerical method for a strongly nonlinear subdiffusion equation.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n arXiv preprint arXiv:2107.10057. 2021.\n \n\n\n\n
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@article{plociniczak2021linear,\n  title={A linear Galerkin numerical method for a strongly nonlinear subdiffusion equation},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={arXiv preprint arXiv:2107.10057},\n  year={2021}\n}\n\n
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\n  \n 2020\n \n \n (8)\n \n \n
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\n \n\n \n \n \n \n \n Hopf bifurcation in a conceptual climate model with ice–albedo and precipitation–temperature feedbacks.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Nonlinear Analysis: Real World Applications, 51: 102967. 2020.\n \n\n\n\n
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@article{plociniczak2020hopf,\n  title={Hopf bifurcation in a conceptual climate model with ice--albedo and precipitation--temperature feedbacks},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Nonlinear Analysis: Real World Applications},\n  volume={51},\n  pages={102967},\n  year={2020},\n  publisher={Pergamon}\n}\n\n
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\n \n\n \n \n \n \n \n Asymptotic analysis of internal relaxation oscillations in a conceptual climate model.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n IMA Journal of Applied Mathematics, 85(3): 467–494. 2020.\n \n\n\n\n
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@article{plociniczak2020asymptotic,\n  title={Asymptotic analysis of internal relaxation oscillations in a conceptual climate model},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={IMA Journal of Applied Mathematics},\n  volume={85},\n  number={3},\n  pages={467--494},\n  year={2020},\n  publisher={Oxford University Press}\n}\n\n
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\n \n\n \n \n \n \n \n Solution and asymptotic analysis of a boundary value problem in the spring–mass model of running.\n \n \n \n\n\n \n Płociniczak, Ł.; and Wróblewska, Z.\n\n\n \n\n\n\n Nonlinear Dynamics, 99(4): 2693–2705. 2020.\n \n\n\n\n
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@article{plociniczak2020solution,\n  title={Solution and asymptotic analysis of a boundary value problem in the spring--mass model of running},\n  author={P{\\l}ociniczak, {\\L}ukasz and Wr{\\'o}blewska, Zofia},\n  journal={Nonlinear Dynamics},\n  volume={99},\n  number={4},\n  pages={2693--2705},\n  year={2020},\n  publisher={Springer Netherlands}\n}\n\n
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\n \n\n \n \n \n \n \n A weighted finite difference method for subdiffusive Black–Scholes model.\n \n \n \n\n\n \n Krzyżanowski, G.; Magdziarz, M.; and Płociniczak, Ł.\n\n\n \n\n\n\n Computers & Mathematics with Applications, 80(5): 653–670. 2020.\n \n\n\n\n
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@article{krzyzanowski2020weighted,\n  title={A weighted finite difference method for subdiffusive Black--Scholes model},\n  author={Krzy{\\.z}anowski, Grzegorz and Magdziarz, Marcin and P{\\l}ociniczak, {\\L}ukasz},\n  journal={Computers \\& Mathematics with Applications},\n  volume={80},\n  number={5},\n  pages={653--670},\n  year={2020},\n  publisher={Pergamon}\n}\n\n
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\n \n\n \n \n \n \n \n Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise.\n \n \n \n\n\n \n Płociniczak, Ł.; and Świtała, M.\n\n\n \n\n\n\n Physica D: Nonlinear Phenomena, 406: 132394. 2020.\n \n\n\n\n
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@article{plociniczak2020asymptotic,\n  title={Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise},\n  author={P{\\l}ociniczak, {\\L}ukasz and {\\'S}wita{\\l}a, Mateusz},\n  journal={Physica D: Nonlinear Phenomena},\n  volume={406},\n  pages={132394},\n  year={2020},\n  publisher={North-Holland}\n}\n\n
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\n \n\n \n \n \n \n \n Off-axis vortex beam propagation through classical optical system in terms of Kummer confluent hypergeometric function.\n \n \n \n\n\n \n Augustyniak, I.; Lamperska, W.; Masajada, J.; Płociniczak, Ł.; and Popiołek-Masajada, A.\n\n\n \n\n\n\n In Photonics, volume 7, pages 60, 2020. MDPI\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@inproceedings{augustyniak2020off,\n  title={Off-axis vortex beam propagation through classical optical system in terms of Kummer confluent hypergeometric function},\n  author={Augustyniak, Ireneusz and Lamperska, Weronika and Masajada, Jan and P{\\l}ociniczak, {\\L}ukasz and Popio{\\l}ek-Masajada, Agnieszka},\n  booktitle={Photonics},\n  volume={7},\n  number={3},\n  pages={60},\n  year={2020},\n  organization={MDPI}\n}\n\n
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\n \n\n \n \n \n \n \n Solvability in Hölder spaces of an integral equation which models dynamics of the capillary rise.\n \n \n \n\n\n \n Okrasińska-Płociniczak, H.; Płociniczak, Ł.; Rocha, J.; and Sadarangani, K.\n\n\n \n\n\n\n Journal of Mathematical Analysis and Applications, 490(1): 124237. 2020.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{okrasinska2020solvability,\n  title={Solvability in H{\\"o}lder spaces of an integral equation which models dynamics of the capillary rise},\n  author={Okrasi{\\'n}ska-P{\\l}ociniczak, Hanna and P{\\l}ociniczak, {\\L}ukasz and Rocha, Juan and Sadarangani, Kishin},\n  journal={Journal of Mathematical Analysis and Applications},\n  volume={490},\n  number={1},\n  pages={124237},\n  year={2020},\n  publisher={Academic Press}\n}\n\n
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\n \n\n \n \n \n \n \n Asymptotic Solution of a Boundary Value Problem for a Spring–Mass Model of Legged Locomotion.\n \n \n \n\n\n \n Okrasińska-Płociniczak, H.; and Płociniczak, Ł.\n\n\n \n\n\n\n Journal of Nonlinear Science, 30(6): 2971–2988. 2020.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{okrasinska2020asymptotic,\n  title={Asymptotic Solution of a Boundary Value Problem for a Spring--Mass Model of Legged Locomotion},\n  author={Okrasi{\\'n}ska-P{\\l}ociniczak, Hanna and P{\\l}ociniczak, {\\L}ukasz},\n  journal={Journal of Nonlinear Science},\n  volume={30},\n  number={6},\n  pages={2971--2988},\n  year={2020},\n  publisher={Springer US}\n}\n\n
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\n  \n 2019\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Communications in Nonlinear Science and Numerical Simulation, 76: 66–70. 2019.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2019derivation,\n  title={Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Communications in Nonlinear Science and Numerical Simulation},\n  volume={76},\n  pages={66--70},\n  year={2019},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n Numerical method for the time-fractional porous medium equation.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n SIAM Journal on Numerical Analysis, 57(2): 638–656. 2019.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2019numerical,\n  title={Numerical method for the time-fractional porous medium equation},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={SIAM Journal on Numerical Analysis},\n  volume={57},\n  number={2},\n  pages={638--656},\n  year={2019},\n  publisher={SIAM}\n}\n\n
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\n  \n 2018\n \n \n (5)\n \n \n
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\n \n\n \n \n \n \n \n Monotonicity, oscillations and stability of a solution to a nonlinear equation modelling the capillary rise.\n \n \n \n\n\n \n Płociniczak, Ł.; and Świtała, M.\n\n\n \n\n\n\n Physica D: Nonlinear Phenomena, 362: 1–8. 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2018monotonicity,\n  title={Monotonicity, oscillations and stability of a solution to a nonlinear equation modelling the capillary rise},\n  author={P{\\l}ociniczak, {\\L}ukasz and {\\'S}wita{\\l}a, Mateusz},\n  journal={Physica D: Nonlinear Phenomena},\n  volume={362},\n  pages={1--8},\n  year={2018},\n  publisher={North-Holland}\n}\n\n
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\n \n\n \n \n \n \n \n Quickest drift change detection in Lévy-type force of mortality model.\n \n \n \n\n\n \n Krawiec, M.; Palmowski, Z.; and Płociniczak, Ł.\n\n\n \n\n\n\n Applied Mathematics and Computation, 338: 432–450. 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{krawiec2018quickest,\n  title={Quickest drift change detection in L{\\'e}vy-type force of mortality model},\n  author={Krawiec, Micha{\\l} and Palmowski, Zbigniew and P{\\l}ociniczak, {\\L}ukasz},\n  journal={Applied Mathematics and Computation},\n  volume={338},\n  pages={432--450},\n  year={2018},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n Existence and uniqueness results for a time-fractional nonlinear diffusion equation.\n \n \n \n\n\n \n Płociniczak, Ł.; and Świtała, M.\n\n\n \n\n\n\n Journal of mathematical analysis and applications, 462(2): 1425–1434. 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2018existence,\n  title={Existence and uniqueness results for a time-fractional nonlinear diffusion equation},\n  author={P{\\l}ociniczak, {\\L}ukasz and {\\'S}wita{\\l}a, Mateusz},\n  journal={Journal of mathematical analysis and applications},\n  volume={462},\n  number={2},\n  pages={1425--1434},\n  year={2018},\n  publisher={Academic Press}\n}\n\n
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\n \n\n \n \n \n \n \n Solution estimates for a system of nonlinear integral equations arising in optometry.\n \n \n \n\n\n \n Okrasiński, W.; and Płociniczak, Ł.\n\n\n \n\n\n\n . 2018.\n \n\n\n\n
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@article{okrasinski2018solution,\n  title={Solution estimates for a system of nonlinear integral equations arising in optometry},\n  author={Okrasi{\\'n}ski, Wojciech and P{\\l}ociniczak, {\\L}ukasz},\n  year={2018}\n}\n\n
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\n \n\n \n \n \n \n \n Numerical method for Volterra equation with a power-type nonlinearity.\n \n \n \n\n\n \n Okrasińska-Płociniczak, H.; and Płociniczak, Ł.\n\n\n \n\n\n\n Applied Mathematics and Computation, 337: 452–460. 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{okrasinska2018numerical,\n  title={Numerical method for Volterra equation with a power-type nonlinearity},\n  author={Okrasi{\\'n}ska-P{\\l}ociniczak, Hanna and P{\\l}ociniczak, {\\L}ukasz},\n  journal={Applied Mathematics and Computation},\n  volume={337},\n  pages={452--460},\n  year={2018},\n  publisher={Elsevier}\n}\n\n
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\n  \n 2017\n \n \n (3)\n \n \n
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\n \n\n \n \n \n \n \n Numerical schemes for integro-differential equations with Erdélyi-Kober fractional operator.\n \n \n \n\n\n \n Płociniczak, Ł.; and Sobieszek, S.\n\n\n \n\n\n\n Numerical Algorithms, 76: 125–150. 2017.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2017numerical,\n  title={Numerical schemes for integro-differential equations with Erd{\\'e}lyi-Kober fractional operator},\n  author={P{\\l}ociniczak, {\\L}ukasz and Sobieszek, Szymon},\n  journal={Numerical Algorithms},\n  volume={76},\n  pages={125--150},\n  year={2017},\n  publisher={Springer US}\n}\n\n
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\n \n\n \n \n \n \n \n Regularization and the inflection point method for sensor signal in gas concentration measurement.\n \n \n \n\n\n \n Płociniczak, ᴌ.; Maciejewska, M.; and Szczurek, A.\n\n\n \n\n\n\n Inverse Problems in Science and Engineering, 25(4): 555–579. 2017.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{plociniczak2017regularization,\n  title={Regularization and the inflection point method for sensor signal in gas concentration measurement},\n  author={P{\\l}ociniczak, ᴌukasz and Maciejewska, Monika and Szczurek, Andrzej},\n  journal={Inverse Problems in Science and Engineering},\n  volume={25},\n  number={4},\n  pages={555--579},\n  year={2017},\n  publisher={Taylor \\& Francis}\n}\n\n
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\n \n\n \n \n \n \n \n Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program.\n \n \n \n\n\n \n Jurlewicz, A.; Nunes, C.; Russo, G.; Rocha, J.; Heilio, M.; Jablonska-Sabuka, M.; Khoury, N.; Hjorth, P.; Serna, S.; and Goetz, T.\n\n\n \n\n\n\n In Progress in Industrial Mathematics at ECMI 2016 19, pages 347–353, 2017. Springer International Publishing\n \n\n\n\n
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@inproceedings{jurlewicz2017modeling,\n  title={Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program},\n  author={Jurlewicz, Agnieszka and Nunes, Claudia and Russo, Giovanni and Rocha, Juan and Heilio, Matti and Jablonska-Sabuka, Matylda and Khoury, Nada and Hjorth, Poul and Serna, Susana and Goetz, Thomas},\n  booktitle={Progress in Industrial Mathematics at ECMI 2016 19},\n  pages={347--353},\n  year={2017},\n  organization={Springer International Publishing}\n}\n\n
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\n  \n 2016\n \n \n (6)\n \n \n
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\n \n\n \n \n \n \n \n Analytical model of the optical vortex microscope.\n \n \n \n\n\n \n Płocinniczak, Ł.; Popiołek-Masajada, A.; Masajada, J.; and Szatkowski, M.\n\n\n \n\n\n\n Applied optics, 55(12): B20–B27. 2016.\n \n\n\n\n
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@article{plocinniczak2016analytical,\n  title={Analytical model of the optical vortex microscope},\n  author={P{\\l}ocinniczak, {\\L}ukasz and Popio{\\l}ek-Masajada, Agnieszka and Masajada, Jan and Szatkowski, Mateusz},\n  journal={Applied optics},\n  volume={55},\n  number={12},\n  pages={B20--B27},\n  year={2016},\n  publisher={Optica Publishing Group}\n}\n\n
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\n \n\n \n \n \n \n \n Transformation of the vortex beam in the optical vortex scanning microscope.\n \n \n \n\n\n \n Płociniczak, Ł.; Popiołek-Masajada, A.; Szatkowski, M.; and Wojnowski, D.\n\n\n \n\n\n\n Optics & Laser Technology, 81: 127–136. 2016.\n \n\n\n\n
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@article{plociniczak2016transformation,\n  title={Transformation of the vortex beam in the optical vortex scanning microscope},\n  author={P{\\l}ociniczak, {\\L}ukasz and Popio{\\l}ek-Masajada, Agnieszka and Szatkowski, Mateusz and Wojnowski, Dariusz},\n  journal={Optics \\& Laser Technology},\n  volume={81},\n  pages={127--136},\n  year={2016},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n Diffusivity identification in a nonlinear time-fractional diffusion equation.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Fractional Calculus and Applied Analysis, 19(4): 843–866. 2016.\n \n\n\n\n
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@article{plociniczak2016diffusivity,\n  title={Diffusivity identification in a nonlinear time-fractional diffusion equation},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Fractional Calculus and Applied Analysis},\n  volume={19},\n  number={4},\n  pages={843--866},\n  year={2016},\n  publisher={De Gruyter}\n}\n\n
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\n \n\n \n \n \n \n \n Optical Vortex Microscope-Analytical Model and its Experimental Verification.\n \n \n \n\n\n \n Popiołek-Masajada, A.; Masajada, J.; and Plociniczak, Ł.\n\n\n \n\n\n\n In Laser Science, pages JW4A–77, 2016. Optica Publishing Group\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@inproceedings{popiolek2016optical,\n  title={Optical Vortex Microscope-Analytical Model and its Experimental Verification},\n  author={Popio{\\l}ek-Masajada, Agnieszka and Masajada, Jan and Plociniczak, {\\L}ukasz},\n  booktitle={Laser Science},\n  pages={JW4A--77},\n  year={2016},\n  organization={Optica Publishing Group}\n}\n\n
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\n \n\n \n \n \n \n \n Analysis of cornea curvature using radial basis functions–Part II: Fitting to data-set.\n \n \n \n\n\n \n Griffiths, G. W; Schiesser, W.; and others\n\n\n \n\n\n\n Computers in Biology and Medicine, 77: 285–296. 2016.\n \n\n\n\n
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@article{griffiths2016analysis,\n  title={Analysis of cornea curvature using radial basis functions--Part II: Fitting to data-set},\n  author={Griffiths, Graham W and Schiesser, WE and others},\n  journal={Computers in Biology and Medicine},\n  volume={77},\n  pages={285--296},\n  year={2016},\n  publisher={Pergamon}\n}\n\n
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\n \n\n \n \n \n \n \n Analysis of cornea curvature using radial basis functions–Part I: Methodology.\n \n \n \n\n\n \n Griffiths, G. W; Schiesser, W.; and others\n\n\n \n\n\n\n Computers in biology and medicine, 77: 274–284. 2016.\n \n\n\n\n
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@article{griffiths2016analysis,\n  title={Analysis of cornea curvature using radial basis functions--Part I: Methodology},\n  author={Griffiths, Graham W and Schiesser, WE and others},\n  journal={Computers in biology and medicine},\n  volume={77},\n  pages={274--284},\n  year={2016},\n  publisher={Elsevier}\n}\n\n
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\n  \n 2015\n \n \n (4)\n \n \n
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\n \n\n \n \n \n \n \n Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Communications in Nonlinear Science and Numerical Simulation, 24(1-3): 169–183. 2015.\n \n\n\n\n
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@article{plociniczak2015analytical,\n  title={Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Communications in Nonlinear Science and Numerical Simulation},\n  volume={24},\n  number={1-3},\n  pages={169--183},\n  year={2015},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n Vortex microscope: analytical model and experiment.\n \n \n \n\n\n \n Masajada, J.; Popiołek-Masajada, A.; Szatkowski, M.; and Plociniczak, Ł.\n\n\n \n\n\n\n In Twelfth International Conference on Correlation Optics, volume 9809, pages 88–98, 2015. SPIE\n \n\n\n\n
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@inproceedings{masajada2015vortex,\n  title={Vortex microscope: analytical model and experiment},\n  author={Masajada, Jan and Popio{\\l}ek-Masajada, Agnieszka and Szatkowski, Mateusz and Plociniczak, {\\L}ukasz},\n  booktitle={Twelfth International Conference on Correlation Optics},\n  volume={9809},\n  pages={88--98},\n  year={2015},\n  organization={SPIE}\n}\n\n
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\n \n\n \n \n \n \n \n High order vortex beam in the optical vortex microscope.\n \n \n \n\n\n \n Płócienniczak, Ł.; Popiołek-Masajada, A.; Szatkowski, M.; and Masajada, J.\n\n\n \n\n\n\n In Laser Beam Shaping XVI, volume 9581, pages 67–74, 2015. SPIE\n \n\n\n\n
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@inproceedings{plocienniczak2015high,\n  title={High order vortex beam in the optical vortex microscope},\n  author={P{\\l}{\\'o}cienniczak, {\\L}ukasz and Popio{\\l}ek-Masajada, Agnieszka and Szatkowski, Mateusz and Masajada, Jan},\n  booktitle={Laser Beam Shaping XVI},\n  volume={9581},\n  pages={67--74},\n  year={2015},\n  organization={SPIE}\n}\n\n
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\n \n\n \n \n \n \n \n Nonlinear parameter identification in a corneal geometry model.\n \n \n \n\n\n \n Płociniczak, ᴌ; and Okrasiński, W\n\n\n \n\n\n\n Inverse Problems in Science and Engineering, 23(3): 443–456. 2015.\n \n\n\n\n
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@article{plociniczak2015nonlinear,\n  title={Nonlinear parameter identification in a corneal geometry model},\n  author={P{\\l}ociniczak, ᴌ and Okrasi{\\'n}ski, W},\n  journal={Inverse Problems in Science and Engineering},\n  volume={23},\n  number={3},\n  pages={443--456},\n  year={2015},\n  publisher={Taylor \\& Francis}\n}\n\n
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\n  \n 2014\n \n \n (4)\n \n \n
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\n \n\n \n \n \n \n \n On a nonlinear boundary value problem modeling corneal shape.\n \n \n \n\n\n \n Płociniczak, Ł.; Okrasiński, W.; Nieto, J. J; and Dominguez, O.\n\n\n \n\n\n\n Journal of Mathematical Analysis and Applications, 414(1): 461–471. 2014.\n \n\n\n\n
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@article{plociniczak2014nonlinear,\n  title={On a nonlinear boundary value problem modeling corneal shape},\n  author={P{\\l}ociniczak, {\\L}ukasz and Okrasi{\\'n}ski, Wojciech and Nieto, Juan J and Dominguez, Oscar},\n  journal={Journal of Mathematical Analysis and Applications},\n  volume={414},\n  number={1},\n  pages={461--471},\n  year={2014},\n  publisher={Academic Press}\n}\n\n
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\n \n\n \n \n \n \n \n Eigenvalue asymptotics for a fractional boundary-value problem.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Applied Mathematics and Computation, 241: 125–128. 2014.\n \n\n\n\n
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@article{plociniczak2014eigenvalue,\n  title={Eigenvalue asymptotics for a fractional boundary-value problem},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Applied Mathematics and Computation},\n  volume={241},\n  pages={125--128},\n  year={2014},\n  publisher={Elsevier}\n}\n\n
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\n \n\n \n \n \n \n \n ODE/PDE analysis of corneal curvature.\n \n \n \n\n\n \n Płociniczak, Ł.; Griffiths, G. W; and Schiesser, W. E\n\n\n \n\n\n\n Computers in Biology and Medicine, 53: 30–41. 2014.\n \n\n\n\n
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@article{plociniczak2014ode,\n  title={ODE/PDE analysis of corneal curvature},\n  author={P{\\l}ociniczak, {\\L}ukasz and Griffiths, Graham W and Schiesser, William E},\n  journal={Computers in Biology and Medicine},\n  volume={53},\n  pages={30--41},\n  year={2014},\n  publisher={Pergamon}\n}\n\n
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\n \n\n \n \n \n \n \n Approximation of the Erdélyi–Kober operator with application to the time-fractional Porous medium equation.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n SIAM journal on applied mathematics, 74(4): 1219–1237. 2014.\n \n\n\n\n
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@article{plociniczak2014approximation,\n  title={Approximation of the Erd{\\'e}lyi--Kober operator with application to the time-fractional Porous medium equation},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={SIAM journal on applied mathematics},\n  volume={74},\n  number={4},\n  pages={1219--1237},\n  year={2014},\n  publisher={Society for Industrial and Applied Mathematics}\n}\n\n
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\n  \n 2013\n \n \n (5)\n \n \n
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\n \n\n \n \n \n \n \n A note on fractional Bessel equation and its asymptotics.\n \n \n \n\n\n \n Okrasiński, W.; and Płociniczak, Ł.\n\n\n \n\n\n\n Fractional Calculus and Applied Analysis, 16: 559–572. 2013.\n \n\n\n\n
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@article{okrasinski2013note,\n  title={A note on fractional Bessel equation and its asymptotics},\n  author={Okrasi{\\'n}ski, Wojciech and P{\\l}ociniczak, {\\L}ukasz},\n  journal={Fractional Calculus and Applied Analysis},\n  volume={16},\n  pages={559--572},\n  year={2013},\n  publisher={SP Versita}\n}\n\n
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\n \n\n \n \n \n \n \n On asymptotics of some fractional differential equations.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n Mathematical Modelling and Analysis, 18(3): 358–373. 2013.\n \n\n\n\n
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@article{plociniczak2013asymptotics,\n  title={On asymptotics of some fractional differential equations},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  journal={Mathematical Modelling and Analysis},\n  volume={18},\n  number={3},\n  pages={358--373},\n  year={2013},\n  publisher={Taylor \\& Francis Group}\n}\n\n
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\n \n\n \n \n \n \n \n Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative.\n \n \n \n\n\n \n Płociniczak, Ł.; and Okrasińska, H.\n\n\n \n\n\n\n Physica D: Nonlinear Phenomena, 261: 85–91. 2013.\n \n\n\n\n
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@article{plociniczak2013approximate,\n  title={Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative},\n  author={P{\\l}ociniczak, {\\L}ukasz and Okrasi{\\'n}ska, Hanna},\n  journal={Physica D: Nonlinear Phenomena},\n  volume={261},\n  pages={85--91},\n  year={2013},\n  publisher={North-Holland}\n}\n\n
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\n \n\n \n \n \n \n \n Regularization of an ill-posed problem in corneal topography.\n \n \n \n\n\n \n Płociniczak, Ł; and Okrasiński, W\n\n\n \n\n\n\n Inverse Problems in Science and Engineering, 21(6): 1090–1097. 2013.\n \n\n\n\n
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@article{plociniczak2013regularization,\n  title={Regularization of an ill-posed problem in corneal topography},\n  author={P{\\l}ociniczak, {\\L} and Okrasi{\\'n}ski, W},\n  journal={Inverse Problems in Science and Engineering},\n  volume={21},\n  number={6},\n  pages={1090--1097},\n  year={2013},\n  publisher={Routledge}\n}\n\n
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\n \n\n \n \n \n \n \n Bessel function model of corneal topography.\n \n \n \n\n\n \n Okrasiński, W.; and Płociniczak, Ł.\n\n\n \n\n\n\n Applied Mathematics and Computation, 223: 436–443. 2013.\n \n\n\n\n
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@article{okrasinski2013bessel,\n  title={Bessel function model of corneal topography},\n  author={Okrasi{\\'n}ski, Wojciech and P{\\l}ociniczak, {\\L}ukasz},\n  journal={Applied Mathematics and Computation},\n  volume={223},\n  pages={436--443},\n  year={2013},\n  publisher={Elsevier}\n}\n\n
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\n  \n 2012\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n A nonlinear mathematical model of the corneal shape.\n \n \n \n\n\n \n Okrasiński, W.; and Płociniczak, Ł.\n\n\n \n\n\n\n Nonlinear Analysis: Real World Applications, 13(3): 1498–1505. 2012.\n \n\n\n\n
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@article{okrasinski2012nonlinear,\n  title={A nonlinear mathematical model of the corneal shape},\n  author={Okrasi{\\'n}ski, Wojciech and P{\\l}ociniczak, {\\L}ukasz},\n  journal={Nonlinear Analysis: Real World Applications},\n  volume={13},\n  number={3},\n  pages={1498--1505},\n  year={2012},\n  publisher={Pergamon}\n}\n\n
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\n \n\n \n \n \n \n \n On fractional Bessel equation and the description of corneal topography.\n \n \n \n\n\n \n Okrasiński, W.; and Płociniczak, Ł.\n\n\n \n\n\n\n arXiv preprint arXiv:1201.2526. 2012.\n \n\n\n\n
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@article{okrasinski2012fractional,\n  title={On fractional Bessel equation and the description of corneal topography},\n  author={Okrasi{\\'n}ski, Wojciech and P{\\l}ociniczak, {\\L}ukasz},\n  journal={arXiv preprint arXiv:1201.2526},\n  year={2012}\n}\n\n
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\n  \n 2010\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n Anomalous nonlinear diffusion in porous media: analytical approximations.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n In 19th European Conference on Mathematics for Industry, volume 118, pages 300, 2010. \n \n\n\n\n
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@inproceedings{plociniczak2010anomalous,\n  title={Anomalous nonlinear diffusion in porous media: analytical approximations},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  booktitle={19th European Conference on Mathematics for Industry},\n  volume={118},\n  pages={300},\n  year={2010}\n}\n\n
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\n \n\n \n \n \n \n \n Numerical methods for nonlocal and nonlinear parabolic equations with applications in hydrology and climatology.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n In 2023 Joint Mathematics Meetings (JMM 2023), . AMS\n \n\n\n\n
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@inproceedings{plociniczak2023numerical,\n  title={Numerical methods for nonlocal and nonlinear parabolic equations with applications in hydrology and climatology},\n  author={P{\\l}ociniczak, {\\L}ukasz},\n  booktitle={2023 Joint Mathematics Meetings (JMM 2023)},\n  organization={AMS}\n}\n\n
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\n \n\n \n \n \n \n \n Metody numeryczne dla nieliniowych i nielokalnych równań parabolicznych wraz z zastosowaniami.\n \n \n \n\n\n \n Płociniczak, Ł.\n\n\n \n\n\n\n . .\n \n\n\n\n
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@article{plociniczakmetody,\n  title={Metody numeryczne dla nieliniowych i nielokalnych r{\\'o}wna{\\'n} parabolicznych wraz z zastosowaniami},\n  author={P{\\l}ociniczak, {\\L}ukasz}\n}\n\n
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