A NEW VARIANT OF FUZZY FRACTIONAL DYNAMIC SYSTEM DRIVEN BY TIME-DEPENDENT VARIATIONAL INEQUALITY
Shengda Zeng, Yunru Bai, Jen‐Chih Yao, Van Thien Nguyen · Fractals · 2022
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.