Volume 56, Number 6, November-December 2022
|Page(s)||2181 - 2196|
|Published online||01 December 2022|
Efficient computation of the Wright function and its applications to fractional diffusion-wave equations
Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale, viale T. Michel 11, 15121 Alessandria, Italy
2 Dipartimento di Matematica, Università di Pisa, via F. Buonarroti 1/C, 56127 Pisa, Italy
* Corresponding author: email@example.com
Accepted: 5 September 2022
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the Laplace transform of a particular expression of the Wright function for which we discuss in detail the error analysis. We also present a code package that implements the algorithm proposed here in different programming languages. The analysis and implementation are accompanied by an extensive set of numerical experiments that validate both the theoretical estimates of the error and the applicability of the proposed method for representing the solutions of fractional differential equations.
Mathematics Subject Classification: 65D20 / 65D30 / 44A10 / 26A33
Key words: Wright function / laplace transform / trapezoidal rule / fractional PDEs
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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