Numerical Accuracy of different types of Linear and Non-Linear Fractional Differential Equations by using Adomian Decomposition method

Abstract

The paper proposes the Adomian Decomposition Method for fractional Differential Equations. The study presented an iterative scheme for a linear and non -linear system of equation scheme for a linear. We introduce new approaches to study of numerical accuracy of linear and non-linear fractional differential equation by using Adomian Decomposition method. Through the numerical test, we can find that the Adomian decomposition method is a powerful tool for solving linear and non-linear fractional differential equations. The numerical results also show the efficiency of this method. The solutions are derived in convergent series form which shows the effectiveness of the method for solving a wide variety of fractional differential equations. All calculation performed by MATLAB Version 2020.