Computational and Numerical Analysis of the Caputo-Type Fractional Nonlinear Dynamical Systems via Novel Transform

Two new methods for handling a system of nonlinear fractional differential equations are presented in this investigation. Based on the characteristics of fractional calculus, the Caputo fractional partial derivative provides an easy way to determine the approximate solution for systems of nonlinear fractional differential equations. These methods provide a convergent series solution by using simple steps and symbolic computation. Several graphical representations and tables provide numerical simulations of the results, which demonstrate the effectiveness and dependability of the current schemes in locating the numerical solutions of coupled systems of fractional nonlinear differential equations. By comparing the numerical solutions of the systems under study with the accurate results in situations when a known solution exists, the viability and dependability of the suggested methodologies are clearly depicted. Additionally, we compared our results with those of the homotopy decomposition method, the natural decomposition method, and the modified Mittag-Leffler function method. It is clear from the comparison that our techniques yield better results than other approaches. The numerical results show that an accurate, reliable, and efficient approximation can be obtained with a minimal number of terms. We demonstrated that our methods for fractional models are straightforward and accurate, and researchers can apply these methods to tackle a range of issues. These methods also make clear how to use fractal calculus in real life. Furthermore, the results of this study support the value and significance of fractional operators in real-world applications.