Resolution of system of Volterra integral equations of the first kind by derivation technique and modified decomposition methods

A solution method for various systems of integral equations of the first kind is presented in this paper. The method starts off by transforming the systems via the application of the Leibnitz’s derivation technique and then employs three different decomposition methods based on the Standard Adomian decomposition method (SADM) for solutions. To demonstrate the efficiency of the proposed method, some illustrative examples are considered and the obtained results indicate that the approach is indeed of practical interest.