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

摘要

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.