Distributed order fractional diffusion equation with fractional Laplacian in axisymmetric cylindrical configuration

被引：25

作者：

Ansari, Alireza ^{[1
]}

Derakhshan, Mohammad Hossein ^{[2
]}

Askari, Hassan ^{[1
]}

机构：

[1] Shahrekord Univ, Fac Math Sci, Dept Appl Math, POB 115, Shahrekord, Iran

[2] Apadana Inst Higher Educ, Dept Ind Engn, Shiraz, Iran

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2022年 / 113卷

关键词：

Fractional diffusion equation; Distributed order; Mittag-Leffler function; Wright function; Laplace transform; GREEN-FUNCTION; TRANSFORMS; POWERS; CALCULUS;

D O I：

10.1016/j.cnsns.2022.106590

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the powers (fractional and natural) of the Laplacian operator in axisymmetric cylindrical geometry. We get the fundamental solution of the distributed order time-fractional diffusion equation with this type of fractional Laplacian and the fractional moment of solution is given. Our study is considered in the plane and half space cases and the roles of the Mittag-Leffler and Wright functions in the structures of solutions are also discussed. (C) 2022 Elsevier B.V. All rights reserved.

引用

页数：14

共 66 条

[1]

Abramowitz M., 1964, Handbook of mathematical functions with formulas, graphs, and mathematical tables, V9th, DOI DOI 10.2307/2282672

[2] SOLVING PARTIAL FRACTIONAL DIFFERENTIAL EQUATIONS USING THE L-A -TRANSFORM [J].