Fundamental solutions of the general fractional‐order diffusion equations

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 resul...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 41; no. 18; pp. 9312 - 9320
Main Authors Yang, Xiao‐Jun, Gao, Feng, Ju, Yang, Zhou, Hong‐Wei
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.12.2018
Subjects
general fractional derivatives
general fractional‐order diffusion equation
general Mittag‐Leffler function
Laplace transforms
Mathematical analysis
Prabhakar function
series solution
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5341