A successive midpoint-based method for the numerical analysis of chaotic systems with local and nonlocal operators

In this study, we examine the uniqueness conditions for solutions of fractal differential equations using the Krasnoselskii-Krein uniqueness theorem. The analysis establishes sufficient criteria that guarantee the existence of unique solutions. Additionally, we employ the successive midpoint method to numerically solve chaotic systems governed by both fractal and global derivatives. To evaluate the effectiveness of the proposed approach, graphical simulations are presented for various derivative orders. These results illustrate the method’s accuracy, stability, and reliability in capturing the intricate dynamics of the considered systems.