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

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.

Automated summary

This article deals with the efficient computation of the Wright function for expressing solutions of fractional differential equations. The proposed algorithm is based on the inversion of the Laplace transform of a specific expression of the Wright function, and its error analysis is discussed in detail. A code package implementing the algorithm in different programming languages is also presented. Extensive numerical experiments are conducted to validate the theoretical error estimates and the applicability of the proposed method.