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 Mikusiński's operational calculus, and utilise this algebraic formalism to solve some fractional differential equations.

Keywords

• fractional integrals
• fractional derivatives
• operational calculus
• fractional differential equations
• mikusiński's operational calculus