special approximation method for solving system of ordinary and fractional integro-differential equations

This paper concerns with some special approximate methods in order to solve the system of ordinary and the fractional integro-differential  equations. the approach that we use begins by a method of converting the fractional integro-differential equations into an integral equation including both volterra and the fredholm parts. then a specific successive approximation technique is  applied to the volterra part. due to the presence of the factorial factor in the denominator of its kernel, the volterra part tends to zero in the next iterations, leading us to discard the volterra's sentence as an error of the  method that we use. the analytical-approximate solution to the problem is then obtained by solving the resulting equation, as a fredholm integral equation of the second kind. this method is applied to the boundary value problems in two distinct cases involving system of ordinary and fractional differential equations.