Triangular functions operational matrix method for solving nonlinear fractional integro-differential equations with weakly singular kernel

In this paper, triangular functions method combining with its operational matrix of fractional integration are applied to the numerical solution of nonlinear fractional Volterra integrodifferential equations with weakly singular kernel. The main purpose of this technique is to transform the initial equation into a nonlinear system of algebraic equations which can be solved easily. In the end, we solve an example by this method and also, by block pulse functions method and Haar wavelets method. The approximate solutions obtained by these methods are compared together.