This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Computer Modeling in Engineering & Sciences ech T Press Science DOI: 10.32604/cmes.2023.026313 ARTICLE On Time Fractional Partial Diferential Equations and Their Solution by Certain Formable Transform Decomposition Method Rania Saadeh 1 , Ahmad Qazza 1 , Aliaa Burqan 1 and Shrideh Al-Omari 2 , * 1 Department of Mathematics, Zarqa University, Zarqa, 13110, Jordan 2 Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Amman, 11134, Jordan *Corresponding Author: Shrideh Al-Omari. Email: shridehalomari@bau.edu.jo Received: 29 August 2022 Accepted: 30 November 2022 ABSTRACT This paper aims to investigate a new efcient method for solving time fractional partial diferential equations. In this orientation, a reliable formable transform decomposition method has been designed and developed, which is a novel combination of the formable integral transform and the decomposition method. Basically, certain accurate solutions for time-fractional partial diferential equations have been presented. The method under concern demands more simple calculations and fewer eforts compared to the existing methods. Besides, the posed formable transform decomposition method has been utilized to yield a series solution for given fractional partial diferential equations. Moreover, several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory. Furthermore, the formable transform decomposition method has been employed for fnding a series solution to a time-fractional Klein-Gordon equation. Over and above, some numerical simulations are also provided to ensure reliability and accuracy of the new approach. KEYWORDS Caputo derivative; fractional diferential equations; formable transform; time-fractional klein-gordon equation; decomposition method 1 Introduction Through the development of science, various phenomena of memory and hereditary properties cannot be well expressed by standard differential equations [1–4]. To address such problems, so many phenomena are described by using fractional differential equations. Indeed, fractional differential equations have been magnificently utilized in modeling various physical and chemical phenomena. Therefore, the mathematical side of fractional differential equations and their solving techniques have been studied by many authors (see, e.g., [5–11]). Meanwhile, different methods have appeared in the contribution of fractional calculus, including homotopy analysis [12,13], fractional transform methods [14–18] and residual power series methods [19–23] as well. Various researchers have combined more than one technique to create new methods, such as the Laplace residual power series method and the ARA residual power series method, to mention but a few. In this study, we create a new method named