A practical guide to Prabhakar fractional calculus

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.

35 pages, 1 figure, Matches the version accepted in FCAA

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Cited by in corpus (27)

• Why fractional derivatives with nonsingular kernels should not be used
• Why the Mittag-Leffler function can be considered the Queen function of the Fractional Calculus?
• Variable-order fractional calculus: a change of perspective
• MOND-like Fractional Laplacian Theory
• A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators
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