International Journal of Engineering and Artificial Intelligence Vol 2 No 1 (2021) 43–59 43 Solving Fuzzy Fractional Nuclear Decay Equations by the Residual Power Series Moath Ali Alshorman 1 , Nurnadiah Zamri 1 , Asia Khalaf Albzeirat 2 1 Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut, Terengganu, Malaysia 2 Department of Mathematics, Mutah University, Mutah, Jordan Corresponding Author: moathuniza@gmail.com Received 12 January 2021, Accepted 14 February 2021, Available online 1 March 2021 1. Introduction The initial form of the fuzzy differential equations appeared through the -suggestions of Chang and Zadeh (Sheldon& Zadeh, 1972) these equations quickly grew in the applications of many sciences, physics, engineering, energy, and other sciences, at the present time, the fuzzy differential equations have overlapped with the fractional differential equations with many applications (Allahviranloo, 2021), and deep complications have emerged to find solutions to many equations, one of the equations with important applications is what is known as the Nuclear Decay Equations (NDEs) as a kind of fractional Riccati differential equations (Khodadadi & Karabacak, 2016 Marakhtanov & Okunev,2018) the solution of this form of equations is extremely important because of its applications in the field of nuclear energy, so in this paper we will put a solution to this type of equations with fuzzy conditions by the RPS (Alshorman et al.., 2018). Therefore, we consider the next form of NDEs as the following: ( ) ( ), 0 1, 0 1, (0) t D yt ay t t y d            (1) Where t D  is the Caputo fractional derivative for order  , a is a variable, and is the count of total radionuclide's existing in any radioactive, It can be observed that Eq.1 is a general formulation of where the initial value d According to the organization of this paper, the first section will include a simple introduction that contains the general form of the equations, while the second section includes the main definitions. Third section include the ABSTRACT This paper deals with the solutions of fuzzy fractional nuclear decay equations (FNDEs) under Caputo H- differentiability by Residual Power Series (RPS). The equations was reformulated under the influence of fuzzy logic. The Residual Power Series has been applied in solving differential equations with fuzzy initial conditions. This method is illustrated by solving two examples. The solution method has shown high efficiency and accuracy in the case of comparison with the exact solution and another method. Keywords: Fuzzy, Fractional Differential Equation, Nuclear Decay Equations, Residual Power Series International Journal of Engineering and Artificial Intelligence (IJEAI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). International Journal of Engineering and Artificial Intelligence Journal home page: http://www.ijeai.com Original article