STABILITY ANALYSIS OF WORM PROPAGATION IN WIRELESS SENSOR NETWORK MODEL UTILIZING FRACTAL-FRACTIONAL OPERATOR

Govindaswamy Gokulvijay (), Sriramulu Sabarinathan, Mohamed Biomy and Sofian Abuelbacher Adam Saad ()
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Govindaswamy Gokulvijay: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulthur 603 203, Tamil Nadu, India
Sriramulu Sabarinathan: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulthur 603 203, Tamil Nadu, India
Mohamed Biomy: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 52571, Saudi Arabia
Sofian Abuelbacher Adam Saad: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-13

Abstract: Wireless sensor networks have been extensively studied for their potential applications in both civil and military domains. However, due to their inherent resource constraints, sensor nodes are highly susceptible to cyber threats, particularly worm attacks, which pose significant security challenges. This study explores the dynamics of potential worm attacks within wireless sensor networks using a compartmental epidemic model. The model analyzes the temporal evolution of worm propagation while effectively capturing both spatial and temporal aspects. We determine the reproduction number and equilibrium of the system, with the local stability assessed using the Jacobian matrix. The linear growth and Lipschitz conditions are used to establish the existence and uniqueness of the solution. Furthermore, the Hyers–Ulam stability of the proposed model is also evaluated within the context of the fractal-fractional operator. Finally, a numerical method is developed to investigate the dynamic behavior of the wireless sensor network model under fractal-fractional orders, providing valuable insights into its robustness and security against potential worm attacks.

Keywords: Epidemic Model; Fractional Derivatives; Hyers–Ulam Stability; Mathematical Model; Numerical Results; Wireless Sensor Network (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401000

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