Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform

Fractal and Fractional

article

Ved Prakash Dubey¹  Jagdev Singh²  Sarvesh Dubey⁴  Devendra Kumar³ 

[1] Faculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University;Department of Mathematics, JECRC University;Department of Computer Science and Mathematics, Lebanese American University;Department of Physics, L.N.D. College, B.R. Ambedkar Bihar University;Department of Mathematics, University of Rajasthan;Department of Mathematics, Kyung Hee University

关键词: Hilfer–Prabhakar fractional derivative;    Cauchy problems;    diffusion equations;    Kharrat–Toma transform;    Mittag–Leffler function26A33;    42B10;    33E12;    34A08;    44A35;   

DOI  :  10.3390/fractalfract7050413

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived. Moreover, we also compute the solution of some Cauchy problems and diffusion equations modeled with the HP fractional derivative via Kharrat–Toma transform. The solutions of Cauchy problems and the diffusion equations modeled with the HP fractional derivative are computed in the form of the generalized Mittag–Leffler function.

【 授权许可】

CC BY