Dynamics of innate immune response to Parkinson’s disease with therapeutic approach using Atangana-Baleanu fractional derivative

This paper presents a fractional variable-order model of Parkinson’s disease using the Atangana-Baleanu fractional derivative to capture complex disease dynamics. The model incorporates therapeutic strategies, allowing it to represent the progression of the disease with greater flexibility than traditional integer-order models. By applying fixed point theory and nonlinear analysis, the study establishes the existence and Ulam-Hyers stability of solutions, ensuring robustness under varied conditions. Numerical simulations demonstrate that the model can efficiently simulate the effects of various treatments, providing insight for decision-makers on optimal intervention strategies.