Some Properties of Prabhakar-type Fractional Calculus Operators

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.

References in corpus (4)

• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Hilfer-Prabhakar Derivatives and Some Applications
• Analytical properties and applications of the Wright function
• On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics

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• Volterra-Prabhakar derivative of distributed order and some applications