Mikusinski's Operational Calculus for Fractional Operators with Different Kernels

Abstract

Mikusinski's operational calculus provides a way of applying the machinery of abstract algebra to the spaces and operators of calculus, thus allowing integro-differential equations to be solved by reducing them to algebraic equations. We summarise the application of this method to several operators of fractional calculus, defined by various convolution kernel functions at different levels of generality, and how the corresponding fractional differential equations can be solved. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)