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.
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