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arXiv · 1805.09398

On Fractional Diffusion-Advection-Reaction Equation In $\mathbb{R}$

V. Ginting·Y. Li
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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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V. Ginting, Y. Li. 2018-05-23. On Fractional Diffusion-Advection-Reaction Equation In $\mathbb{R}$. https://arxiv.org/abs/1805.09398

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