increase in complexity and sophistication. Early viruses, such as the Creeper program of the 1970s, were relatively harmless, often serving as experimental projects [5]. However, these early examples quickly gave way to more malicious creations. Notable viruses like Stuxnet demonstrated the potential for viruses to inflict massive economic damage and even target critical infrastructure, highlighting the real-world consequences of these digital threats [6]. Modern viruses employ increasingly sophisticated techniques to evade detection and maintain persistence within digital environments. For example, polymorphic and metamorphic viruses dynamically alter their code, making it extremely difficult for traditional signature-based detection systems to identify and neutralize them [7]. This constant evolution necessitates a continuous adaptation of cybersecurity defense mechanisms. In the ongoing battle against computer viruses, studies have turned to mathematical modeling as a critical tool for understanding virus propagation and developing effective containment strategies [8]. Drawing inspiration from biological epidemiology, various methods have been adapted from traditional epidemic models to analyze and predict the spread of viruses within computer networks [9]. Among these, the Susceptible-Infected (SI) model is a widely used framework for examining virus behavior. However, the standard integer-order versions of these models often fall short when attempting to capture long-term dependencies and memory effects frequently observed in real-world cyber threats [10]. Standard models frequently employ simplifications of intricate interactions and fail to account for the historical context of virus spread. This limitation has led to a growing interest in fractional-order models, which incorporate historical interactions and offer a more detailed and precise depiction of virus propagation [11]. By integrating memory effects, fractional-order models offer a more realistic and powerful tool for predicting and mitigating the impact of evolving digital threats. In parallel, some studies have analyzed the spread of actual computer viruses such as Code Red, Slammer, Conficker, and Stuxnet, using parameterized statistical distributions to fit real outbreak data [12]. These works provide a valuable benchmark for validating the qualitative behavior of theoretical models, including those based on fractional calculus. Fractional calculus, extending classical calculus, extends differentiation and integration concepts to non-integer orders. This mathematical framework offers unique advantages for modeling complex systems by incorporating memory effects and hereditary properties [13]. Unlike traditional integer-order derivatives, which analyze only local changes, fractional derivatives consider the influence of past events on the present and future behavior of a system [14]. This property makes fractional calculus highly effective in studying systems with long-term dependencies, such as the spread of viruses in digital networks [15]. The application of fractional calculus in mathematical modeling has gained traction within a diverse range of fields, notably physics, biology, engineering, and finance [16]. In epidemiology and cybersecurity, fractional models have been particularly successful in capturing the history-dependent nature of disease and virus propagation [17]. By incorporating fractional derivatives, it is possible to better understand how past infections influence current and future outbreaks, leading to more accurate predictive models [18]. In discrete systems, fractional calculus provides a robust framework for analyzing systems that evolve in discrete time steps, making it highly suitable for modeling digital networks and computational processes. Unlike continuous-time models, which may not fully capture digital environments' complexities, discrete fractional models offer a more precise approach to studying virus spread in cyberspace.