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On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian

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Abstract

This paper investigates the structure of solutions to the BVP of a class of fractional ordinary differential equations involving both fractional derivatives (R-L or Caputo) and fractional Laplacian with variable coefficients. This family of equations generalize the usual fractional diffusion equation and fractional Laplace equation.

We provide a deep insight to the structure of the solutions shared by this family of equations. The specific decomposition of the solution is obtained, which consists of the “good” part and the “bad” part that precisely control the regularity and singularity, respectively. Other associated properties of the solution will be characterized as well.

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  1. Department of Mathematics and Statistics, University of Nevada, Reno 1664 N. Virginia Street, Reno, NV, 89557, USA

    Yulong Li

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Li, Y. On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian. Fract Calc Appl Anal 24, 1571–1600 (2021). https://doi.org/10.1515/fca-2021-0066

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