Analytical scheme for the solution of multi-higher Fractional Order Linear Integro-Differential Equations of Fredholm type with Variable Coefficients using Adomian and Modified Adomian Decomposition Methods

Abstract

In this paper, Adomian decomposition method (ADM) and modified Adomian decomposition method (MADM) has been introduced to find the exact or approximate solution to a wide class of multi-higher fractional order linear integro-differential problems of Fredholm type with variable coefficients in which the fractional derivative is described in the Caputo sense. In this methods the solution of a functional equation is considered as the sum of infinite series of components usually converging to the solution based on the appearance of the noise terms, where a closed form solution is not obtainable, a truncated number of terms is usually used for numerical purposes. Finally, Numerical experiment prepared that modified Adomian decomposition solutions converges faster than Adomian decomposition solution and by several examples illustrate these considerations.