General fractional calculus and Prabhakar's theory

TL;DR

This paper explores the integration of Prabhakar's three-parameter Mittag-Leffler function into the broader framework of general fractional calculus, highlighting theoretical implications and potential advancements.

Contribution

It provides a conceptual analysis of how Prabhakar's theory fits within the general fractional calculus paradigm, expanding the theoretical foundation.

Findings

Insights into the unification of Prabhakar's function with general fractional calculus

Implications for the development of more flexible fractional models

Potential pathways for future research in generalized fractional operators

Abstract

General fractional calculus offers an elegant and self-consistent path toward the generalization of fractional calculus to an enhanced class of kernels. Prabhakar's theory can be thought of, to some extent, as an explicit realization of this scheme achieved by merging the Prabhakar (or, three-parameter Mittag-Leffler) function with the general wisdom of the standard (Riemann-Liouville and Caputo) formulation of fractional calculus. Here I discuss some implications that emerge when attempting to frame Prabhakar's theory within the program of general fractional calculus.