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On the Fractional Diffusion-Advection-Reaction Equation in ℝ

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Wyoming, 1000 E. University Avenue, Dept. 3036, Laramie, Wyoming, USA

    Victor Ginting & Yulong Li

  2. Science and Mathematics, Singapore University of Technology and Design, 8 Somapah Road, Singapore, 487372, Singapore

    Yulong Li

Authors
  1. Victor Ginting
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  2. Yulong Li
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Correspondence to Yulong Li.

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Ginting, V., Li, Y. On the Fractional Diffusion-Advection-Reaction Equation in ℝ. FCAA 22, 1039–1062 (2019). https://doi.org/10.1515/fca-2019-0055

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  • DOI: https://doi.org/10.1515/fca-2019-0055

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