A Fractional Study for Solving the Smoking Model and the Chaotic Engineering Model

In this study, a novel scheme for the Caputo-Fabrizio fractional derivative (CFFD) is employed to solve the fractional smoking model and a chaotic electrical model. Illustrations comparing the results between the proposed method and RK4 have been presented. It has been discovered that the proposed method yields solutions equivalent to the approximate solutions produced by the other methods. Therefore, the strategy can be generalized to other systems to obtain more precise results. The use of this Caputo-Fabrizio fractional derivative scheme has remarkable potential in engineering disciplines. Its ability to detect chaos in diverse systems-like weather patterns, mechanical vibrations, and financial markets-promises a revolutionary approach to managing complex, nonlinear dynamics. Additionally, its equivalence to established techniques, such as RK4, in control systems and signal processing offers avenues for more accurate modeling and control, enhancing system stability. In biomedical engineering, its adaptability to disease modeling could lead to significant advancements in predicting and managing various health conditions. This scheme's demonstrated reliability and versatility across different systems suggest its potential as a go-to tool for solving intricate challenges in engineering and science in the future.