Well-posedness of an initial value problem for fractional diffusion equation with Caputo-Fabrizio derivative

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:375

Article

Nguyen Huy Tuan¹  Zhou, Yong^2,3 

[1] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau 999078, Peoples R China

[3] Xiangtan Univ, Fac Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

关键词: Fractional derivatives and integrals;    Caputo-Fabrizio fractional derivative;    Blow up;    Well-posedness;    Regularity estimates;   

DOI  :  10.1016/j.cam.2020.112811

来源: Elsevier

【 摘 要 】

In this paper, we consider the following Cauchy problem of space-time fractional diffusion equations {(CF)D(0,t)(alpha)u + (-L)(s)u = G(t, x: u), in (0,T] X Omega, u(t, x) = 0, on (0, T] X partial derivative Omega, u(0, x) = u(0)(x), in Omega, The time fractional derivative is taken in the sense of Caputo-Fabrizio type. We derive representation of solutions by using Laplace transform and we further establish the existence and uniqueness of the mild solution. Both the linear case and the nonlinear case with globally Lipschitz assumption, we investigate the regularity of the mild solution. For the case of locally Lipschitz assumption, we study the existence of local mild solutions to the problem and then a blow-up alternative is established. We also consider the problem of continuous dependence with respect to initial data. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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