On the Numerical Computation of the Mittag–Leffler Function-Reference-Cited by-同舟云学术

On the Numerical Computation of the Mittag–Leffler Function

Published:2019-07-12 Issue:6 Volume:20 Page:725-736
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Ortigueira Manuel D.¹,Lopes António M.²^ORCID,Tenreiro Machado José³

Affiliation:

1. Center for Technology and Systems – UNINOVA and DEE , NOVA School of Science and Technology of NOVA University of Lisbon , Porto , Portugal

2. Faculty of Engineering , University of Porto , Rua Dr. Roberto Frias , Porto 4200–465 , Portugal

3. Dept. of Electrical Engineering , Institute of Engineering, Polytechnic of Porto , Rua Dr. Antonio Bernardino de Almeida, 431 , Porto 4249-015 , Portugal

Abstract

Abstract The Mittag–Leffler function (MLF) plays an important role in many applications of fractional calculus, establishing a connection between exponential and power law behaviors that characterize integer and fractional order phenomena, respectively. Nevertheless, the numerical computation of the MLF poses problems both of accuracy and convergence. In this paper, we study the calculation of the 2-parameter MLF by using polynomial computation and integral formulas. For the particular cases having Laplace transform (LT) the method relies on the inversion of the LT using the fast Fourier transform. Experiments with two other available methods compare also the computational time and accuracy. The 3-parameter MLF and its calculation are also considered.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modelling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2018-0358/pdf

Reference28 articles.

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