In this work, a numerical approach based on the modified Taylor's technique for derive the analytical approximate solutions is applied for systems of Fredholm integro-differential equations. The solution is calculated in the form of a rapidly convergent series with easily computable components using symbolic computation software. The results obtained depend on Taylor's series expansions and they reproduce to the exact solutions when the solutions are polynomials. Numerical examples are presented and discussed quantitatively to illustrate the method. The results show the potentiality, the generality, and the superiority of our algorithm for solving such systems.

The aim of the present analysis is present a relatively new analytical treatment, called residual power series (RPS) method, for solving system of fuzzy initial value problems under strongly generalized differentiability. The technique methodology provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. The results reveal that the present simulated method is very effective, straightforward and powerful methodology to solve such fuzzy equations.