Fractal-Fractional Modeling and Analysis of Monkeypox Disease Using Atangana-Baleanu Derivative

In this study, we formulate a deterministic mathematical model to describe the transmission dynamics of the monkeypox virus using fractal and fractional-order differential equations. The model incorporates all possible interactions influencing disease propagation within the population. Our analysis primarily focuses on the stability of fractal–fractional derivatives, aiming to establish the existence and uniqueness of solutions through the fixed-point theorem. Additionally, we examine Ulam-Hyers stability and other significant findings related to the proposed model. To enhance numerical accuracy, we employ Lagrange polynomial interpolation for computational approximations. Finally, graphical simulations for various fractal–fractional orders are presented to validate the model’s effectiveness and demonstrate its practical relevance.