On the Fractional Diffusion-Advection-Reaction Equation in $ℝ$. Ginting, V. & Li, Y. Fractional Calculus & Applied Analysis, 22(4):1039-1062, 2019. ![On the Fractional Diffusion-Advection-Reaction Equation in $ℝ$ [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex We present an analysis of existence, uniqueness, and smoothness of the solution to a class of fractional ordinary differential equations posed on the whole real line that models a steady state behavior of a certain anomalous diffusion, advection, and reaction. The anomalous diffusion is modeled by the fractional Riemann-Liouville differential operators. The strong solution of the equation is sought in a Sobolev space defined by means of Fourier Transform. The key component of the analysis hinges on a characterization of this Sobolev space with the Riemann-Liouville derivatives that are understood in a weak sense. The existence, uniqueness, and smoothness of the solution is demonstrated with the assistance of several tools from functional and harmonic analyses.
@article{glifcaa19,
title = "{O}n the {F}ractional {D}iffusion-{A}dvection-{R}eaction {E}quation in $\mathbb{R}$",
journal = "Fractional Calculus \& Applied Analysis",
volume = "22",
number="4",
pages = "1039-1062",
year = "2019",
issn = "1311-0454",
author = "Victor Ginting and Yulong Li",
doi ="https://doi.org/10.1515/fca-2019-0055",
url ="https://www.degruyter.com/view/j/fca.2019.22.issue-4/fca-2019-0055/fca-2019-0055.xml?format=INT",
keywords = "Riemann-Liouville fractional operators, fractional diffusion, advection, reaction, weak fractional derivative, strong solution, regularity, infinite domain",
abstract = "We present an analysis of existence, uniqueness, and smoothness of the solution to a class of fractional ordinary differential equations posed on the whole real line that models a steady state behavior of a certain anomalous diffusion, advection, and reaction. The anomalous diffusion is modeled by the fractional Riemann-Liouville differential operators. The strong solution of the equation is sought in a Sobolev space defined by means of Fourier Transform. The key component of the analysis hinges on a characterization of this Sobolev space with the Riemann-Liouville derivatives that are understood in a weak sense. The existence, uniqueness, and smoothness of the solution is demonstrated with the assistance of several tools from functional and harmonic analyses."
}
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