A numerical study of a new non-linear fractal fractional mathematical model of malicious codes propagation in wireless sensor networks

Abstract

This paper presents a novel non-linear fractal fractional mathematical model for analyzing the spread of malicious codes in wireless sensor networks (WSNs). The model incorporates fractional calculus and non-linear interactions among nodes in a WSN. It is based on the Fractal-Fractional (FF) operator, a powerful mathematical tool that combines fractional and fractal calculus. This study explores the potential of fractional derivatives in addressing computer virus-related issues and proposes a model that elucidates the spread of viruses in a vulnerable system and potential countermeasures. The Fractal-Fractional operator is utilized to fractionalize the model, and the fixed point theory of Schauder and Banach is applied to establish the existence and uniqueness of a solution. Numerical simulations, employing MATLAB and the Adams-Bashforth method, validate the effectiveness of the proposed model in capturing the propagation dynamics of malicious codes. Ulam-Hyers stability techniques are also employed for stability analysis. The model's insights contribute to enhancing the security and robustness of WSNs against malicious code propagation, paving the way for more secure network designs. This research provides a unique perspective on analyzing the dynamics of WSNs and underscores the significance of fractional derivatives in addressing security threats in network systems.