QUALITATIVE AND STABILITY ANALYSIS WITH LYAPUNOV FUNCTION OF EMOTION PANIC SPREADING MODEL INSIGHT OF FRACTIONAL OPERATOR

Peiluan Li (), Changjin Xu, Muhammad Farman, Ali Akgul and Yicheng Pang ()
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Peiluan Li: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, P. R. China
Changjin Xu: ��Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, P. R. China
Muhammad Farman: ��Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan§Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard PC
Ali Akgul: �Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard PC
Yicheng Pang: *School of Mathematics and Statistics, Art and Science Faculty, Guizhou University of Finance and Economics, Guiyang 550025, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-24

Abstract: In an emergency, fear can spread among crowds through one-on-one encounters, with negative societal consequences. The purpose of this research is to create a novel theoretical model of fear (panic) spread in the context of epidemiology during an emergency using the fractal fractional operator. For quantitative analysis, the system’s boundedness and positivity are checked. According to the Arzela Ascoli theorem, the model is completely continuous. As a result of the discovery of Schauder’s fixed point, it has at least one solution. The existence and uniqueness of the concerned solution have been examined using the fixed point theory technique. Numerical simulations are used to demonstrate the accuracy of the proposed techniques using a generalized form of Mittag-Leffler kernel with a fractal fractional operator. Finally, simulations are utilized to represent the spread of group emotional contagion (spontaneous spread of emotions and related behaviors) dynamically.

Keywords: Panic Spreading Model; Lyapunov Stability; Unique Solution; Qualitative Analysis; Mittag-Leffler Kernel; Fixed-point Theory (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400115

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