Foundations of generalized Prabhakar-Hilfer fractional calculus with applications

George A. Anastassiou

doi:10.4067/S0719-06462021000300423

DOI:

https://doi.org/10.4067/S0719-06462021000300423

Abstract

Here we introduce the generalized Prabhakar fractional calculus and we also combine it with the generalized Hilfer calculus. We prove that the generalized left and right side Prabhakar fractional integrals preserve continuity and we find tight upper bounds for them. We present several left and right side generalized Prabhakar fractional inequalities of Hardy, Opial and Hilbert-Pachpatte types. We apply these in the setting of generalized Hilfer calculus.

Keywords

Prabhakar fractional calculus , Hilfer fractional calculus , fractional Hardy , Opial and Hilbert-Pachpatte inequalities

George A. Anastassiou Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

Pages: 423–440
Date Published: 2021-12-01
Vol. 23 No. 3 (2021)

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