Hyers-Ulam Stability of Fractional Differential Equations Using West Nile Virus

In this paper, we use the Atangana-Baleanu Caputo derivative to design and assess a fractional-order infection model for West Nile virus. The model offers insights into the evolution of the virus and takes into account its intricate dynamics of transmission. We investigate the system’s qualitative behavior and prove existence and uniqueness findings using fixed-point theory. Additionally, we examine the suggested model’s stability in terms of Hyers-Ulam stability. Euler’s approach for the Atangana-Baleanu integral is used to numerically simulate the fractional-order model in order to visualize the effects of different parameters. The theoretical findings are verified, and the impact of fractional-order derivatives on the dynamics of the system is demonstrated using MATLAB. The study emphasizes the use of fractional calculus in epidemiological modeling, which offers a more realistic depiction of the spread of illness in the actual world.