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

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

Published:2023-05-20 Issue:5 Volume:7 Page:413
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Dubey Ved Prakash¹,Singh Jagdev²³,Dubey Sarvesh⁴,Kumar Devendra³⁵⁶^ORCID

Affiliation:

1. Faculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki 225003, Uttar Pradesh, India

2. Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India

3. Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon

4. Department of Physics, L.N.D. College, B.R. Ambedkar Bihar University, Muzaffarpur, Motihari 845401, Bihar, India

5. Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India

6. Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

Abstract

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.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/5/413/pdf

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5. Hilfer, R. (2008). Threefold Introduction to Fractional Derivatives. Anomalous Transport: Foundations and Applications, Germany Publishing.

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