A Fractional Cubic Spline Approach for Solving Models of Dynamical System

This article presents a novel numerical approach for solving dynamic system models using fractional cubic splines. The proposed method leverages the smoothness and flexibility of fractional cubic splines to approximate solutions of differential equations. By constructing fractional cubic polynomials, we develop a numerical scheme that ensures high accuracy and stability in capturing the complex behaviors inherent in dynamic systems. The effectiveness of the method is demonstrated through numerical experiments on benchmark problems, showcasing its superiority over traditional spline-based techniques in terms of convergence and computational efficiency. The results highlight the potential of fractional cubic splines as a robust tool for the numerical analysis of dynamic systems. MSC 2010 Classifications: 26A33, 11S82, 65Dxx, 97Nxx.