Fractional-order analysis of a fear-induced ecoepidemiological predator–prey model with optimal control and bifurcation dynamics

We propose and analyze a fractional-order ecoepidemiological predator-prey model that incorporates disease transmission within the prey population and predator-induced fear effects. The model is formulated using the Caputo fractional derivative to capture memory-dependent dynamics. Fundamental properties, including positivity, boundedness, and existence of solutions, are established. Equilibrium points are derived and their local stability is investigated using the Matignon criterion. Numerical bifurcation analysis reveals transitions between stable equilibria and oscillatory regimes under variations of key biological parameters. An optimal control problem is formulated to reduce infection levels and intervention costs, and necessary optimality conditions are obtained via the fractional Pontryagin Maximum Principle. Numerical simulations demonstrate that fractional dynamics and fear effects enhance system stability and reduce control effort.