Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets

In this paper, a numerical method is proposed to solve a class of nonlinear variable order fractional differential equations (FDEs). The idea is to use Legendre wavelets functions and operational matrices. First, a family of piecewise functions is proposed, based on which the variable order fractional derivatives of Legendre wavelets functions are easy to calculate. Second, operational matrices are derived to transform the studied FDEs into a system of algebraic equations. Then, numerical solutions are obtained by solving these equations. Finally, numerical examples are presented to demonstrate the accuracy of the proposed method.