Walsh functions and their applications for solving nonlinear fractional-order Volterra integro-differential equation

In this article, we extended an efficient computational method based on Walsh operational matrix to find an approximate solution of nonlinear fractional order Volterra integro-differential equation. First, we present the fractional Walsh operational matrix of integration and differentiation. Then by applying this method, the nonlinear fractional Volterra integro-differential equation is reduced into a system of algebraic equation. The benefits of this method are the low-cost of setting up the equations without applying any projection method such as collocation, Galerkin, etc. The results show that the method is very accuracy and efficiency.