Efficient Treatment of Some Important Fractal-Fractional Models: Theoretical and Numerical Study
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.6774Keywords:
Banks' competition model (BCM), Optimal control, Brusselator system, Fractal-fractional derivative; Picard's theorem; Numerical integration; RK4M.Abstract
In this study, we investigate two fundamental fractal-fractional (FF) models: the competitive dynamics among Egyptian banks and the Brusselator system. For the banking model, optimal control strategies are proposed to mitigate profit downturns during crises, such as the COVID-19 pandemic, through a system of four fractional differential equations. Recognizing the
slow convergence of traditional numerical methods, an efficient integration technique is developed to simulate both models with enhanced accuracy and computational efficiency. The simulation results reveal the dynamic behaviors of the studied systems for various FF-operator values, confirming the robustness and precision of the proposed approach when compared with the classical fourth-order Runge–Kutta method (RK4M). The presented technique offers a simple yet powerful framework for modeling and analyzing complex FF-based dynamical systems.
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Copyright (c) 2025 Mohamed Adel, M. M. Khader, Dragan Pamucar, Hijaz Ahmad
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