Fundamental solutions of the general fractional-order diffusion equations

被引：96

作者：

Yang, Xiao-Jun ^{[1
,2
]}

Gao, Feng ^{[1
]}

Ju, Yang ^{[1
,3
]}

Zhou, Hong-Wei ^{[3
]}

机构：

[1] China Univ Min & Technol, State Key Lab Geomech & Deep Underground Engn, Xuzhou 221116, Jiangsu, Peoples R China

[2] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao, Peoples R China

[3] China Univ Min & Technol, State Key Lab Coal Resources & Safe Min, Beijing, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 18期

基金：

中国国家自然科学基金;

关键词：

general fractional derivatives; general fractional-order diffusion equation; general Mittag-Leffler function; Prabhakar function; series solution; DERIVATIVES; CALCULUS; MODELS;

D O I：

10.1002/mma.5341

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, the general fractional-order diffusion equations within the negative Prabhakar kernel are considered for the first time. With the aid of the Laplace transform, the series solutions for the problems with the general Mittag-Leffler functions are discussed in detail. The obtained results are efficient in the description of the anomalous behaviors of the diffusive process.

引用

页码：9312 / 9320

页数：9

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