An operational calculus formulation of fractional calculus with general analytic kernels

Abstract

Fractional calculus with analytic kernels provides a general setting of integral and derivative operators that can be connected to Riemann-Liouville fractional calculus via convergent infinite series. We interpret these operators from an algebraic viewpoint, using Mikusinski's operational calculus, and utilise this algebraic formalism to solve some fractional differential equations.