REGULARIZATION OF CAUCHY PROBLEM FOR 2D TIME-FRACTIONAL DIFFUSION EVOLUTION EQUATIONS

Tran Thanh Binh (), Nguyen Phuc Binh (), Bui Dinh Thang () and Le Dinh Long
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Tran Thanh Binh: Faculty of Mathematics and Applications, Sai Gon University, Vietnam
Nguyen Phuc Binh: Faculty of Mathematics and Applications, Sai Gon University, Vietnam
Bui Dinh Thang: Faculty of Mathematics and Applications, Sai Gon University, Vietnam
Le Dinh Long: Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam3Faculty of Technology, Van Lang University, Ho Chi Minh City, Vietnam

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-25

Abstract: In this work, we focus on an initial value problem for a class of 2D time-fractional diffusion evolution equations with Riemann–Liouville fractional derivative. There are three new results in this paper. First of all, the existence and ill-posedness result (in the sense of Hadamard) in three cases which are consisting of homogeneous, inhomogeneous, and nonlinear problems are considered. Next, by using the Fourier truncation method, we show that regularized problems are well-posed. Finally, some demonstrated examples are presented to test the proposed method.

Keywords: Fractional Diffusion Equation; Riemman–Liouville Derivative; Ill-Posedness; Quasi-Boundary Value Method; Fourier Truncation Method (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401818

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DOI: 10.1142/S0218348X22401818

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