A CAPUTO FRACTIONAL LOTKA-VOLTERRA MODEL FOR COMPETITIVE OPINION DYNAMICS: STABILITY ANALYSIS AND DATA-DRIVEN VALIDATION

Competitive opinion dynamics in socio-economic systems often exhibit memory and history-dependent interactions that cannot be adequately captured by classical integer-order models. In this paper, we propose a Caputo fractional-order Lotka-Volterra framework to describe the competition between two interacting opinions and provide a rigorous mathematical analysis of the resulting system. By reformulating the model in an equivalent Volterra integral form, we establish existence and uniqueness of solutions and conduct a local stability analysis based on the Jacobian matrix and the Matignon criterion.The analysis shows that the coexistence equilibrium is asymptotically stable for $0