Numerical research of nonlinear system of fractional Volterra–Fredholm integral–differential equations via Block-Pulse functions and error analysis

Abstract

In this study, a numerical scheme for approximating the solutions of nonlinear system of fractional-order Volterra–Fredholm integral–differential equations (VFIDEs) has been proposed. This method is based on the orthogonal functions defined over $\left[0,1\right)$ combined with their operational matrices of integration and fractional-order differentiation. The main characteristic behind this approach is that it reduces such problems to a linear system of algebraic equations. In addition the error analysis of the system is investigated in detail. Lastly, several numerical examples are presented to test the effectiveness and feasibility of the given method.