Atangana-Baleanu Fractal-Fractional Operator for Analyzing Dengue Fever Dynamics

Abstract

This research develops a deterministic mathematical model for dengue fever transmission using fractal-fractional order differential equations. The proposed model comprises eight compartments, classifying individuals into human and vector populations. By utilizing fixed-point theory, we demonstrate the existence and uniqueness of solutions within the system. We apply fundamental theorems in fractal-fractional calculus alongside the fractional Adams-Bashforth method to obtain approximate solutions. Simulations are performed across various fractional orders and fractal dimensions, offering comparisons with traditional integer-order models. Incorporating fractalfractional derivatives enhances the model's ability to capture complex disease dynamics, including memory effects and long-term behavior. This approach provides valuable insights into epidemic control and helps refine inderivatives reveal intricate disease patterns, making them essential for un (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.