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

Year 2021, Volume: 5 Issue: 2, 203 - 214, 30.06.2021

Rachid Belgacem Ahmed Bokhari Boualem Sadaoui

https://doi.org/10.31197/atnaa.828468

Cited By: 1

Abstract

In this paper, we are interested on the Shehu transform of both Prabhakar and Hilfer–Prabhakar fractional derivative and its regularized version. These results are presented in terms of Mittag-Leffler type function and also utilized to obtain the solutions of some Cauchy type problems, such as Space-time Fractional Advection-Dispersion equation and Generalized fractional Free Electron Laser (FEL) equation, at which Hilfer-Prabhakar fractional derivative of fractional order and its regularized version are involved.

Keywords

Hilfer–Prabhakar derivatives, Prabhakar integrals, Mittag–Leffler functions, Shehu transform

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