Mikusi?ski’s Operational Calculus Applied in General Classes of Fractional Calculus

Abstract

Mikusi?ski’s operational calculus is an algebraic formalism for integral and derivative operators, constructed in the mid 20th century, which can be used for solving differential equations. It is formally similar to the method of Laplace transforms, but applicable to a bigger set of problems due to its setting in a larger function space. In the 1990s, this formalism was extended to fractional integral and derivative operators and used to solve fractional differential equations. Current research is extending the method to more general types of fractional-calculus operators, introducing new function spaces and techniques to handle such generalised settings. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.