Original Article International Journal of Fuzzy Logic and Intelligent Systems Vol. 22, No. 1, March 2022, pp. 23-47 http://doi.org/10.5391/IJFIS.2022.22.1.23 ISSN(Print) 1598-2645 ISSN(Online) 2093-744X A New Approach to Solving Fuzzy Quadratic Riccati Differential Equations Moa’ath N. Oqielat 1 , Ahmad El-Ajou 1 , Zeyad Al-Zhour 2 ■ , Tareq Eriqat 1 , and Mohammed Al-Smadi 3,4 1 Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt, Jordan 2 Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia 3 Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun, Jordan 4 Nonlinear Dynamics Research Centre (NDRC), Ajman University, Ajman, UAE Abstract In this paper, we present in detail the power series solutions to fuzzy quadratic Riccati differential equations (QRDEs) along with a suitable fuzzy constant through an interactive derivative, more specifically, the Hukuhara-strongly generalized differentiability (H-SGD) based on our new technique. This technique is called the Laplace residual power series (LRPS) method, and it mainly depends on a new expansion and the combination of the Laplace transform technique with the residual power series method. To validate the accuracy of our proposed algorithm, numerous examples were examined numerically and graphically, and we compared the results of the optimal homotopy asymptotic (OHA), multiagent neural network (MNN), and fourth-order Runge-Kutta (RK-4) methods with the LRPS method at γ =1. Keywords: Fuzzy-valued function, Strongly generalized differentiability, Quadratic Riccati differential equation, Laplace residual power series method, Laplace and inverse transforms Received: Jun. 4, 2021 Revised : Sep. 5, 2021 Accepted: Nov. 1, 2021 Correspondence to: Zeyad Al-Zhour (zeyad1968@yahoo.com) ©The Korean Institute of Intelligent Systems cc This is an Open Access article distrib- uted under the terms of the Creative Com- mons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc / 3.0/) which permits unrestricted non- commercial use, distribution, and reproduc- tion in any medium, provided the original work is properly cited. 1. Introduction Fuzzy set theory is an important topic in the study and modeling of many real-life problems re- lated to numerous physical phenomena and dynamical processes, such as astronomy, quantum mechanics, chromodynamics, quantum optics, electronic mechanisms, electronic-controlled systems, the modeling of anomalous hydraulic diffusion systems, and population dynam- ics models [1–14]. Moreover, several problems in applied mathematics that are associated with biology, medicine, physics, and technology can be modeled using fuzzy differential equations [1–6,15–17]. Fuzzy set theory has been explored since the 1920s; however, the term fuzzy derivative was introduced by Chang and Zadeh [15]. Subsequently, Dubois and Prade [16] proposed the fuzzy differential calculus concept. Many researchers have recently presented other results and notations for fuzzy mapping [18–21]. Moreover, Bede and his colleagues [22,23] defined strongly generalized differentiability (SGD) as a fuzzy-valued function (FVF). In general, it is not straightforward to obtain the exact solution for these types of problems because of the difficulties involved; therefore, reliable numerical techniques are needed, including a reliable numerical algorithm for handling fuzzy integral equations of the second kind in the Hilbert spaces [4], a residual power series (RPS) for solving uncertain Riccati differential equations 23 |