Some Properties of Prabhakar-type Fractional Calculus Operators

TL;DR

This paper investigates properties of Prabhakar fractional calculus operators, including derivatives and extensions, deriving inequalities and exploring connections with probability theory.

Contribution

It introduces new properties and inequalities for Prabhakar operators and explores their relationships with probability theory.

Findings

Derived Opial- and Hardy-type inequalities for Prabhakar operators

Analyzed properties of regularized and Hilfer--Prabhakar derivatives

Explored connections between Prabhakar calculus and probability theory

Abstract

In this paper we study some properties of the Prabhakar integrals and derivatives and of some of their extensions such as the regularized Prabhakar derivative or the Hilfer--Prabhakar derivative. Some Opial- and Hardy-type inequalities are derived. In the last section we point out on some relationships with probability theory.