A class of time-fractional diffusion equations with generalized fractional derivatives

被引：7
|
作者：
Alikhanov, Anatoly A. [1 ]
Huang, Chengming [2 ]
机构：
[1] North Caucasus Fed Univ, North Caucasus Ctr Math Res, Pushkin str 1, Stavropol 355017, Russia
[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 414卷
基金：
俄罗斯基础研究基金会;
关键词：
Caputo fractional derivative; Erdelyi-Kober fractional derivative; Hadamard fractional derivative; Generalized fractional derivative; Fractional diffusion equation; BOUNDARY-VALUE-PROBLEMS; VARIABLE-ORDER; NUMERICAL-METHOD; OPERATORS; SCHEMES;
D O I：
10.1016/j.cam.2022.114424
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider generalized fractional derivatives, which are characterized by a scale function and a weight function. It is proposed to replace the time variable with a new variable, associated with the scale and weight functions, which allows us to reduce the problems for equations with generalized fractional derivatives to problems for equations with the usual fractional derivative. The equations obtained after the above change of variables are quite well studied, so that one can apply well-known effective numerical methods and use the reverse substitution to find solutions to the original problems. (C) 2022 Elsevier B.V. All rights reserved.
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页数：6
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