Browsing by Author "Chan, Chee Seng"

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An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty
(Asme, 2017) Salahshour, Soheil; Chan, Chee Seng; Baleanu, Dumitur; Ahmadian, Ali
In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge-Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.
Citation - WoS: 55
Citation - Scopus: 68
Numerical Solutions of Fuzzy Differential Equations by an Efficient Runge-Kutta Method With Generalized Differentiability
(Elsevier, 2018) Salahshour, Soheil; Chan, Chee Seng; Baleanu, Dumitru; Ahmadian, Ali
In this paper, an extended fourth-order Runge-Kutta method is studied to approximate the solutions of first-order fuzzy differential equations using a generalized characterization theorem. In this method, new parameters are utilized in order to enhance the order of accuracy of the solutions using evaluations of both f and f', instead of using the evaluations of f only. The proposed extended Runge-Kutta method and its error analysis, which guarantees pointwise convergence, are given in detail. Furthermore, the accuracy and efficiency of the proposed method are demonstrated in a series of numerical experiments. (C) 2016 Elsevier B.V. All rights reserved.
Citation - WoS: 3
Citation - Scopus: 5
Toward the Existence of Solutions of Fractional Sequential Differential Equations With Uncertainty
(Ieee, 2015) Ahmadian, Ali; Chan, Chee Seng; Baleanu, Dumitru; Salahshour, Soheil
The main study of this paper is focused on the solutions of a class of fuzzy sequential fractional differential equations in the form of (D-0(x)beta y)' (x) = b(x)y(x), where (D-0(x)beta y) (x) is the fuzzy Riemann-Liouville derivative of order beta is an element of(0, 1). On this subject, a new fuzzy complete metric space is introduced. Finally, we proof the existence and uniqueness of our solution using the contraction principle.