Foundations of generalized Prabhakar-Hilfer fractional calculus with applications

  • George A. Anastassiou Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
Keywords: Prabhakar fractional calculus, Hilfer fractional calculus, fractional Hardy, Opial and Hilbert-Pachpatte inequalities


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.


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How to Cite
G. A. Anastassiou, “Foundations of generalized Prabhakar-Hilfer fractional calculus with applications”, CUBO, vol. 23, no. 3, pp. 423–440, Dec. 2021.