Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform

In this paper, the Kharrat–Toma transforms of Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and regularized version HP derivative are derived. Moreover, we also compute solution some Cauchy problems diffusion equations modeled with via transform. The solutions computed in form generalized Mittag–Leffler function.