Application of Legendre wavelet in nonlinear fractional differential equations

In order to obtain a numerical solution for nonlinear differential equations of fractional order,this study obtains Legendre wavelet through Legendre polynomial.Subsequently,it derives the integral operational matrix of fractional order of Legendre wavelet through block pulse functions.Furthermore,the nonlinear differential equations are transformed into a nonlinear system of algebraic equations using the properties of block pulse functions and the integral operational matrix of fractional order of Legendre wavelet.Therefore,the numerical solution of original equations can be obtained.The numerical example demonstrates the effectiveness and feasibility of the method proposed.