A practical guide to Prabhakar fractional calculus
| Autor: | Federico Polito, Roberto Garra, Ivano Colombaro, Francesco Mainardi, Roberto Garrappa, Andrea Giusti, Marina Popolizio |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Scheme (programming language)
Anomalous physical phenomena Generalization media_common.quotation_subject Words and Phrases: Mittag-Leffler type functions 010103 numerical & computational mathematics 01 natural sciences 010305 fluids & plasmas Development (topology) 33E12 26A33 65R10 34K37 60G22 Prabhakar function 0103 physical sciences numerical methods Classical Analysis and ODEs (math.CA) FOS: Mathematics Calculus Prabhakar fractional calculus stochastic processes Complex Variables (math.CV) 0101 mathematics Function (engineering) computer.programming_language Mathematics media_common Stochastic process Mathematics - Complex Variables Applied Mathematics Probability (math.PR) Fractional calculus Mathematics - Classical Analysis and ODEs Key (cryptography) computer Analysis Mathematics - Probability |
| Popis: | 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 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|