Research Article Solution of Space-Time Fractional Differential Equations Using Aboodh Transform Iterative Method Michael A. Awuya , 1 Gbenga O. Ojo , 2 and Nazim I. Mahmudov 1 1 Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Famagusta, T.R. North Cyprus via Mersin 10, Turkey 2 Department of Information System Engineering, Faculty of Engineering Cyprus West University, Famagusta, T.R. North Cyprus via Mersin 10, Turkey Correspondence should be addressed to Nazim I. Mahmudov; nazim.mahmudov@emu.edu.tr Received 8 June 2022; Accepted 18 July 2022; Published 22 September 2022 Academic Editor: Arzu Akbulut Copyright © 2022 Michael A. Awuya 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. A relatively new and efficient approach based on a new iterative method and the Aboodh transform called the Aboodh transform iterative method is proposed to solve space-time fractional differential equations, the fractional order is considered in the Caputo sense. is method is a combination of the Aboodh transform and the new iterative method and gives the solution in series form with easily computable components. e nonlinear term is easily handled by the new iterative method, to affirm the simplicity and performance of the proposed method, five examples were considered, and the solution plots were presented to show the effect of the fractional order. e outcome reveals that the approach is accurate and easy to implement. 1. Introduction Fractional Calculus can be described as the field of math- ematics that consists of ordinary and partial derivatives of positive noninteger order. It is the generalization of classical integral and differential equations [1, 2]. One major at- tractive property of fractional calculus is the nonlocal property. Recently, various problems in Biology and Physics has been modeled with fractional order derivative, an analytical solution of the Fornberg–Whithan equation was presented in [3], fractional model of the Rosenau–Hyman equation which is a KdV-like equation was considered in [4], for application of fractional derivative to Biology population model see [5], the numerical study of HIV-1 infection of CD4+ T-cell was presented in [6], Caputo–Fabrizio frac- tional model of photocatalytic degradation of dyes was studied in [7], a wavelet based numerical scheme for frac- tional order SEIR epidemic of measles by using Genocchi polynomials was presented in [8], and the investigation of fractional order susceptible-infected-recovered epidemic model of childhood disease was presented in [9]. erefore, it is extremely important to find an effective method of solving fractional differential equations, as only the solutions can give a better comprehension of the underlying problems. Many researchers have presented different methods for solving fractional differential equations such as reproducing kernel discretization method [10], Chebyshev wavelet col- location method, [11] Tichonov regularization method [12], Chebyshev collocation method, [13] q-homotopy analysis Shehu transform method [14], Fractional differential transform, [15] Fractional variational iterational method [16], and iterative Laplace transform method [17]. In 2016, the new iterative method was presented by Daftardar–Gejji and Jafari to solve functional equations [18], but now the iterative method has been used to solve many integral and fractional order differential equations. [5, 19, 20] But most of these methods considered a single term time-fractional order differential equations. In this paper, the main objective is to extend the Aboodh transform iterative method to solve space-time fractional differential equations with more than a single term fractional Hindawi Journal of Mathematics Volume 2022, Article ID 4861588, 14 pages https://doi.org/10.1155/2022/4861588