Efficient computation of the Wright function and its applications to fractional diffusion-wave equations

TL;DR

This paper introduces an efficient algorithm for computing the Wright function, crucial for solving fractional differential equations, supported by error analysis, implementation in multiple languages, and extensive numerical validation.

Contribution

It presents a novel algorithm for Wright function computation with detailed error analysis and a multi-language code package for solving fractional differential equations.

Findings

The algorithm accurately computes the Wright function in relevant cases.

Numerical experiments validate the error estimates and effectiveness of the method.

The implementation supports multiple programming languages.

Abstract

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.