A Two-Step Conformable Fractional Iterative Method with Stability and Applications to Nonlinear Problems

Abstract

In this paper, a two-step iterative method based on conformable fractional derivatives is proposed for solving nonlinear equations. The convergence analysis confirms that the method achieves fourth-order convergence. Numerical experiments on real-world problems reveal that the method significantly reduces the number of iterations compared to classical schemes. The method is also tested on several important models, including the Van der Waals equation, blood flow dynamics, population growth laws, chemical engineering models, and Planck's radiation law, demonstrating its wide applicability. Furthermore, the basin of attraction analysis shows improved stability and efficiency, highlighting the method's potential as a reliable alternative for nonlinear problem-solving.