A practical guide to Prabhakar fractional calculus-Reference-Cited by-同舟云学术

A practical guide to Prabhakar fractional calculus

Published:2020-02-01 Issue:1 Volume:23 Page:9-54
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Giusti Andrea¹,Colombaro Ivano²,Garra Roberto³,Garrappa Roberto⁴⁵,Polito Federico⁶,Popolizio Marina⁷⁵,Mainardi Francesco⁸

Affiliation:

1. Department of Physics & Astronomy , Bishop’s University , 2600 College Street QC J1M 1Z7 , Sherbrooke , Canada

2. Department of Information and Communication Technologies , Universitat Pompeu Fabra , C/Roc Boronat 138 , Barcelona , Spain

3. Department of Statistical Sciences , Sapienza University of Rome , Piazzale Aldo Moro 5, 00185 , Roma , Italy

4. Department of Mathematics , University of Bari , Via E. Orabona 4, 70126 , Bari , Italy

5. INdAM Research group GNCS , Rome , Italy

6. Department of Mathematics , University of Torino , Via Carlo Alberto 10, 10123 , Torino , Italy

7. Department of Electrical and Information Engineering , Polytechnic University of Bari , Via E. Orabona 4, 70126 , Bari , Italy

8. Department of Physics and Astronomy , University of Bologna , Via Irnerio 46, 40126 , Bologna , Italy

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0002/pdf

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