Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems

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Original research article

Author(s):

Belgacem Rachid^a, Bokhari Ahmed^b, Sadaoui Boualem^c

^aFaculty of Exact and Computer Sciences, Department of Mathematics, Laboratory of Mathematics and its Applications (LMA), Hassiba Benbouali University, Chlef, Algeria.
^bLaboratory of Pure and Applied Mathematics, Department of Mathematics, Abdelhamid Ibn Badis University, Mostaganem, Algeria.
^cLaboratory of LESI, Djilali Bounaama University, Khemis Miliana, Algeria.

Advances in the Theory of Nonlinear Analysis and its Applications 5 (2), 203-214.

Received: November 19, 2020

Accepted: March 17, 2021

Published: March 20, 2021

Abstract

In this paper, we are interested in the Shehu transform of both Prabhakar and Hilfer–Prabhakar fractional derivatives and its regularized version. These results are presented in terms of Mittag–Leffler type functions and also utilized to obtain the solutions of some Cauchy type problems, such as space–time fractional advection–dispersion equations and generalized fractional Free Electron Laser (FEL) equations, at which Hilfer–Prabhakar fractional derivatives of fractional order and its regularized version are involved.

Keywords: Hilfer–Prabhakar derivatives; Prabhakar integrals; Mittag–Leffler functions; Shehu transform.

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APA Style

Belgacem, R., Bokhari, A., & Sadaoui, B. (2021). Shehu transform of Hilfer-Prabhakar fractional derivatives and applications on some Cauchy type problems. Advances in the Theory of Nonlinear Analysis and its Application , 5 (2), 203-214.