Solution Techniques Based on Adomian and Modified Adomian Decomposition for Nonlinear Integro-Fractional Differential Equations of the Volterra-Hammerstein Type

Abstract

This paper efficiently applies the Adomian Decomposition Method and Modified Adomian Decomposition Method as computational techniques to locate the semi-analytical solution or semi-approximate solution for the considered nonlinear Integro Differential Equations for the fractional-order (IFDE) of the Volterra-Hammerstein (V-H) type, in which the higher-multi fractional derivative is described in the Caputo sense.In this procedure, we radically change the IFDE’s of V-H type into some iterative algebraic equations and the solution of this equations is considered as the sum of the countless sequence of components typically converging to the solution based on the noise terms where a closed-form solution is not obtainable, a truncated number of terms is usually used for numerical purposes.Finally, examples are prepared to illustrate these considerations.