Adomaian decomposition method for solving impulsive fractional differential equations

Abstract

In this paper we apply the adomian decomposition method for solving impulsive fractional differential equations with caputo derivative, this is a powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. At the end we illustrate the proposed method by an example.

An Implementation of the Generalized Differential Transform Scheme for Simulating Impulsive Fractional Differential Equations

“…is given in [52,53] by y(t) � e − t when β � 1. Using the characteristics of the generalized differential transformation of order α, (30) can be transformed to the following recurrence relation:…”

“…A block-by-block numerical method is constructed for the impulsive fractional ordinary differential equations by carrying out a series of numerical examples in [29]. In [30], the Adomian decomposition method was applied to solve impulsive nonclassical type differential equations with the Caputo fractional operator. Very recently, a number of studies in the direction of efficiency and performance of various computational methods have been given by researchers [31][32][33][34][35][36][37][38][39].…”