Future Challenges in the Fractional-Order Dynamical Systems: From Mathematics to Applications

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Original Research
09 August 2023
Modeling and analysis of the addiction of social media through fractional calculus
Meshal Shutaywi
5 more and 
Oana Dumitrascu
Illustration of the solution pathways of (A) exposed individuals, (B) addicted individuals, and (C) recovered individuals of the recommended system with fractional order 1.0, 0.9, 0.8, where the arrow shows a decrease in the addiction level with the decrease in fractional parameter.

Social media addiction (SMA) is the excessive use of social media platforms, resulting in negative consequences for individuals. It is characterized by an uncontrollable urge to use social media, leading to negative effects in human's life. This study aims to construct a mathematical model to conceptualize the transmission dynamics of SMA and explore the underlying mechanisms of this harmful addiction in the framework of fractional derivative. The fundamentals of fractional calculus are listed for examining the model. Equilibrium points are identified, and the reproduction parameter R0 is computed to understand the dynamics of SMA spread. Stability analysis of the equilibria is performed, and the impact of various input parameters is numerically investigated. The existence and uniqueness of the proposed SMA model are demonstrated through simulations, which also study the intricate dynamics with respect to different input factors. To develop effective control strategies, the system's dynamical behavior is examined, and the influence of fractional derivative order on fluctuations is explored. This research offers a range of suggestions aimed at reducing the occurrence of social media addiction.

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Original Research
05 May 2023

To explore malware propagation mechanisms in networks and to develop optimal strategies for controlling the spread of malware, we propose a susceptible-unexposed-infected-isolation-removed epidemic model. First, we establish a non-linear dynamic equation of malware propagation. Then, the basic reproductive number is derived by using the next-generation method. Finally, we carry out numerical simulations to observe the malware spreading in WSNs to verify the obtained theoretical results. Furthermore, we investigate the communication range of the nodes to make the results more complete. The optimal range of the nodes is designed to control malware propagation.

2,653 views
9 citations
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