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Cauchy Problem for General Time Fractional Diffusion Equation

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Abstract

In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei [11]. First, the existence, the positivity and the long time behavior of solutions of the diffusion equation without source term are established by using the Fourier analysis technique. Then, based on the representation of the solution of the inhomogenous linear ordinary differential equation with the general Caputo-type operator, the general diffusion equation with source term is studied.

MSC 2010: Primary 35R11; Secondary 35A01, 35B40, 35E15, 45K05

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Authors and Affiliations

  1. Faculty of Mathematics, Kim Il Sung University, Ryomyong Street, Daesong District, Pyongyang, Korea

    Chung-Sik Sin

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  1. Chung-Sik Sin
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Correspondence to Chung-Sik Sin.

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Sin, CS. Cauchy Problem for General Time Fractional Diffusion Equation. Fract Calc Appl Anal 23, 1545–1559 (2020). https://doi.org/10.1515/fca-2020-0077

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  • DOI: https://doi.org/10.1515/fca-2020-0077

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