Approximate solution for multi-higher nonlinear fractional Volterra- Fredhlom Integro-Differential Equations

Abstract

In this paper finds semi-approximate solutions for nonlinear Integro-Differential Equations of fractional order (FIDEs) of the Volterra-Fredholm Hammerstein (VFH) type, where the higher-order fractional derivative is defined in the Caputo sense, by effectively using the Adomian Decomposition Method and the Modified Adomian Decomposition Method as computational techniques. This method involves converting VF-H type FIDEs into iterative algebraic equations. In this approach, the answer to these equations is the product of an endless series of terms, which usually converges to the solution given by the noise terms. For numerical reasons, a reduced number of terms is utilised when a closed-form solution cannot be found. Lastly, these notions are illustrated using examples.