Abstract
Symmetry analysis is an effective tool for understanding differential equations, particularly when analyzing equations derived from mathematical concepts. This paper is concerned with an impulsive fractional differential equation (IFDE) with a deviated argument. We implement two techniques, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM), for solving IFDEs. In these schemes, we obtain the solutions in the form of a convergent power series with easily computed components. This paper also discusses the existence and uniqueness of solutions using the Banach contraction principle. This paper presents a numerical comparison between the two methods for solving IFDEs. We illustrate the proposed methods with a few examples and find their numerical solutions. Moreover, we show the graph of numerical solutions via MATLAB. The numerical results demonstrate that the ADM approach is quite accurate and readily implemented.