A practical guide to Prabhakar fractional calculus

By Andrea Giusti, Ivano Colombaro, Roberto Garra, Roberto Garrappa, Federico Polito, Marina Popolizio, Francesco Mainardi. Fractional Calculus and Applied Analysis, 2020

170 citations recorded by the source corpus.

Abstract The Mittag–Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from the three-parameter generalization of this function, known as the Prabhakar function. Specifically, after reviewing key historical events that led to the discovery and modern development of this peculiar function, we discuss how the latter allows one to introduce an enhanced scheme for fractional calculus. Then, we summarize the progress in the application of this new general framework to physics and renewal processes. We also provide a collection of results on the numerical evaluation of the Prabhakar function.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4b560e9a2dc809743f4ec9520c98346793c35d75

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Why fractional derivatives with nonsingular kernels should not be used (2020, methodology): “We refer to [7] for a complete treatment of the Prabhakar fractional calculus.”