Memory -dependent fake news dissemination and control: A fractional SVEIR model with stability analysis

• Fractional-order SVEIR model to monitor and control misinformation propagation in OSNs. • Existence, uniqueness, and stability assessments of proposed model. • Interpretation of the epidemiological reproduction number to govern the spreading possibility of misinformation inside OSNs. • Simulations to validate the proposed model effectiveness in monitoring misinformation spread. • Comparative analysis of the proposed model with the existing model. Online social networks (OSNs) have emerged as the primary platform for global information exchange and discussion, connecting people while sharing both true and false news, including rumors. Users frequently have challenges distinguishing among fact, fake news, misinformation, disinformation, and rumors on ONS. These challenges arise due to perceptual uncertainty, which makes it challenging to identify reliable information accurately. Today, the uncontrolled spread of misinformation on online social media has become a major societal problem, influencing public opinion and decision-making across political, social, and economic contexts worldwide. This paper employs the fractional-order SVEIR epidemic model to analyze misinformation propagation dynamics using the Caputo fractional derivative to represent non-local and memory-dependent information dissemination. To characterize the dynamical behavior of information propagation, this work has incorporated the concept of equilibrium points in systems and undertakes detailed stability assessments using the proposed mathematical model. Moreover, this study derives and rigorously analyzes the basic reproduction number R 0 as a critical epidemiological threshold that determines the potential for misinformation propagation within online social networks. The proposed work shows that a stable, rumor-free equilibrium occurs when R 0 < 1 , indicating subcritical transmission, while an endemic equilibrium state occurs when misinformation persists in the community. Also, derive an approximate analytical solution for the proposed model using the Homotopy Perturbation Transform Method (HPTM). The validity and resilience of the proposed model have established by comprehensive theoretical proofs and computational simulations.