In this study, we explore the solution of a nonlinear system of fractional integro-differential equations based on the operational matrix method. We have modified the operational matrix method to accommodate such systems and have streamlined the resulting algebraic system in a practical manner. Instead of dealing with a system of [Formula: see text] equations, we have simplified the problem to finding the solution for a set of [Formula: see text] nonlinear equations. Here, m represents the number of block pulse fu…