Sadaoui BoualemBokhari AhmedBelgacem Rachid2021-07-112021-07-112021https://repository.univ-msila.dz/handle/123456789/24810In 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.Hilfer Prabhakar derivatives, Prabhakar integrals, Mittag Le er functions, Shehu transform 2010 MSC: 44A35, 26A33, 42B10, 33E12.Article