Mikusinski’s Operational Calculus for Prabhakar Fractional Calculus

Mikusinski operational calculus is a powerful yet underappreciated theory, enabling differential equations to be solved using abstract algebra. We realise the fractional integrals and derivatives of Prabhakar type within Mikusi´ nski’s theory, by defining them onnewfunction spaces and using their fundamental properties such as semigroup and series formulae.This algebraic framework allows us to construct explicit solutions for multi-term multi-order fractional differential equations, including the general linear constant-coefficient fractional differential equation posed using Prabhakar operators. Keywords: operational calculus, fractional differential equations, Mikusinski’s operational calculus, Prabhakar fractional calculus