Research Article An Implementation of the Generalized Differential Transform Scheme for Simulating Impulsive Fractional Differential Equations Zaid Odibat , 1 Vedat Suat Erturk , 2 Pushpendra Kumar , 3 Abdellatif Ben Makhlouf , 4 and V. Govindaraj 3 1 School of Basic Sciences and Humanities, German Jordanian University, Amman 11180, Jordan 2 Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun 55139, Turkey 3 Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India 4 Department of Mathematics, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia Correspondence should be addressed to Abdellatif Ben Makhlouf; abmakhlouf@ju.edu.sa Received 8 October 2021; Revised 12 December 2021; Accepted 27 March 2022; Published 16 May 2022 Academic Editor: Muhammad Shoaib Anwar Copyright © 2022 Zaid Odibat et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this research study, the generalized differential transform scheme has been applied to simulate impulsive differential equations with the noninteger order. One specific tool of the implemented scheme is that it converts the problems into a recurrence equation that finally leads easily to the solution of the considered problem. e validity and reliability of this method have successfully been accomplished by applying it to simulate the solution of some equations. It is shown that the considered method is very suitable and efficient for solving classes of fractional-order initial value problems for impulsive differential equations and might find wide applications. 1. Introduction Present, impulsive differential equations are treated as a basic system to explore the structures of various phenomena that are subjected to unexpected variations in their states. Many evolution processes which are simulated in applied sciences are defined by differential equations with the im- pulse effect. e theory and applications addressing such problems have been reported [1–6]. Recently, some inter- esting solutions’ existence results for impulsive differential equations have been explored largely; we suggest the reader to [7–11] and the papers therein. Over the last few years, the applications of fractional derivatives are sharply increasing and a huge quantity of mathematical systems has been explored by using these operators in different regions of science and engineering [12–18]. In the theory of fractional calculus, we talk about the noninteger orders of differential operators. e frac- tional calculus is just a generalization of classical calculus and uses similar methods and features, but is more useful in the application field. e memory effects and hereditary natures of different types of processes and materials can be studied by fractional-order operators much more accurately. ese operators involve the complete history of that function in the given domain or span, which we say memory effects. at is why fractional-order operators are the best fit to describe dynamical systems or various real-life problems. Also, the nonlocal characteristic is one of the beauties of fractional operators. is justifies that the future state of a model depends not only upon the present stage but also upon all past states. All features make the importance of noninteger order systems and that is why an active area of research. Nowadays, impulsive fractional differential equations, as generalizations of impulsive classical differential equations, are applied to model various important dynamical phe- nomena containing evolutionary structures specified by abrupt variations of the position at particular instants. Some Hindawi Mathematical Problems in Engineering Volume 2022, Article ID 8280203, 11 pages https://doi.org/10.1155/2022/8280203