Fractal-fractional modeling and stability analysis of pine wilt disease dynamics
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Date
2025
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Abstract
In this article, we have constructed a compartmental mathematical model employing fractal
fractional operators to investigate the dynamics of pine wilt disease. The model comprises
six nonlinear ordinary differential equations, representing six compartments for individuals
categorized as susceptible, exposed, and infected. Furthermore, we restructured the model
by applying methodologies that are based on fractional calculus and fractal theory, one can
gain significant insights into the intricacies of pine wilt disease transmission. The model’s
essential properties, that is existence and uniqueness were analysed using the Banach and
Leray-Schauder theorems. We study the stability of the fractional model by applying the
Ulam-Hyers stability conditions. Additionally, computational techniques for the model in frac
tal-fractional cases are formulated using an iterative numerical approach like the fractional
Adams-Bashforth methodology. Finally, we presented a comprehensive simulation con
ducted to validate the theoretical findings. The results are simulated to correspond to vari
ous fractional order values (θ
1
) and fractal dimensions (θ
2
) using MATLAB