FRACTAL–FRACTIONAL APPROACHES TO COMPUTER VIRUS CONTROL IN SCALE-FREE NETWORK STRUCTURES

Abstract

This study develops a novel fractal–fractional (FF) model using the Caputo derivative to describe computer virus propagation dynamics in networked environments. The model incorporates memory effects and fractal geometry to accurately simulate virus transmission across complex networks. Fixed-point theory establishes solutions’ existence and uniqueness, while stability analysis ensures robustness. Numerical simulations demonstrate the efficacy of targeted interventions, such as antivirus deployment in high-degree network hubs. The proposed framework highlights the potential of FF derivatives for enhancing our understanding of virus dynamics and informing control strategies. This work bridges a critical gap in the study of computer viruses using fractal and fractional calculus. It provides tools for robust analysis and mitigation in interconnected systems.