A numerical method based on fractional-order generalized Taylor wavelets for solving distributed-order fractional partial differential equations

In this paper, we propose a numerical method for solving distributed-order fractional partial differential equations (FPDEs). For this method, we first introduce fractional-order generalized Taylor wavelets (FOGTW). An estimation for the error of the approximation is also studied. In addition, by using the regularized beta function we give a formula for determining the Riemann-Liouville fractional integral operator for the FOGTW. Combining this formula with the Gauss-Legendre quadrature, we obtain a numerical method for solving distributed-order FPDEs. Several illustrative examples are given to show the applicability and the accuracy of the proposed method. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This paper presents a numerical method for solving distributed-order fractional partial differential equations by introducing fractional-order generalized Taylor wavelets and studying the estimation of the approximation error. A formula for determining the Riemann-Liouville fractional integral operator for the wavelets is provided using the regularized beta function, and combined with Gauss-Legendre quadrature to obtain the numerical method. Several illustrative examples are given to demonstrate the applicability and accuracy of the proposed method.