A NEW VARIANT OF FUZZY FRACTIONAL DYNAMIC SYSTEM DRIVEN BY TIME-DEPENDENT VARIATIONAL INEQUALITY

Shengda Zeng, Yunru Bai (), Jen-Chih Yao () and Nguyen van Thien ()
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Shengda Zeng: Key Laboratory of Complex System Optimization and Big Data Processing, Guangxi Colleges and Universities, Yulin Normal University, Yulin 537000, Guangxi, P. R. China
Yunru Bai: ��School of Science, Guangxi University of Science and Technology, Liuzhou 545006, Guangxi, P. R. China
Jen-Chih Yao: ��Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Nguyen van Thien: �Department of Mathematics, FPT University, Education Zone, Hoa Lac High-Tech Park, Km29 Thang Long Highway, Thach That Ward, Hanoi, Vietnam

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-13

Abstract: The primary goal of this paper is to study a nonlinear fuzzy fractional dynamic system (FFDS) involving a time-dependent variational inequality. We use the monotone argument and Knaster–Kuratowski–Mazurkiewicz (KKM) theorem to prove that the variational system of FFDS is solvable and its solutions become a bounded, closed and convex set. Employing this result together with Bohnenblust–Karlin fixed point theorem and Filippov implicit function, we show the existence of a mild solution to FFDS.

Keywords: Fuzzy Fractional Dynamic System; Existence; KKM Theorem; Measurable Selection; Fixed Point Theorem (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401740

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