Stability and Reproduction Dynamics in Fractional-Order Reaction-Diffusion Models of HIV/AIDS

This research focuses on introducing fractional-order derivatives to an HIV/AIDS mathematical model in order to provide a good representation of disease dynamics. The central point of this work is evaluating the stability of equilibrium points through the use of fractional calculus with an important attention to the role of the basic reproductive number R₀ in determining its impact on system stability. The fractional-order Lyapunov framework will be utilized in investigating stability conditions and clarifying their relationship. In addition, essential analytical properties such as the existence, positivity, and boundedness of solutions will be examined and explored to support the theoretical finding. Numerical simulations will be studied to give additional insights into the spread of disease and demonstrate the contribution of fractional calculus in epidemic modeling.