Alpert wavelet system for solving fractional nonlinear Fredholm integro-differential equations

In this paper, we rst construct Alpert wavelet system and propose a computa- tional method for solving a fractional nonlinear Fredholm integro-differential equa- tion. Then we create an operational matrix of fractional integration and use it to simplify the equation to a system of algebraic equations. By using Newtons iter- ative method, this system is solved, and then solution of the fractional nonlinear Fredholm integro-differential equations is achieved. Thresholding parameter is used to increase the sparsity of matrix coecients and the speed of computations. Fi- nally, the method is demonstrated by examples and the compared results with CAS wavelet method show that our proposed method is more effective and accurate.