Solving Prabhakar differential equations using Mikusinski's operational calculus

Abstract

We study the structure and operators of Prabhakar fractional calculus, in particular the operators of Caputo type, using the machinery of Mikusinski's operational calculus. This algebraic framework allows us to construct explicit solutions for Prabhakar-type fractional differential equations, including the general (incommensurate, multi-order) linear constant-coefficient fractional differential equation posed using Caputo-type Prabhakar derivatives.