Legendre wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order

In order to obtain a numerical solution for nonlinear Fredholm integro-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 Fredholm integro-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 results show that with the increase of points,the precision of numerical solution is increasing.The numerical example demonstrates the effectiveness and feasibility of the method proposed.