On the Numerical Computation of the Mittag-Leffler Function

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Manuel D. Ortigueira (Author) Other; António Mendes Lopes (Author) FEUP; José Tenreiro Machado (Author) Other

Journal

Title: International Journal of Nonlinear Sciences and Numerical Simulation

Vol. 20 No. 6

Pages: 725-736

ISSN: 1565-1339

Publisher: Walter De Gruyter

Indexing

ISI Web of Knowledge - 11 Citations

Scopus - 13 Citations

Other information

Authenticus ID: P-00Q-WM7

DOI: 10.1515/ijnsns-2018-0358

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12