Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems
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Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
Université de M'sila
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-Le er 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.
Description
Keywords
Hilfer Prabhakar derivatives, Prabhakar integrals, Mittag Le er functions, Shehu transform 2010 MSC: 44A35, 26A33, 42B10, 33E12.