ON COMPUTATIONAL EFFICIENT HIGHER-ORDER FRACTIONAL SCHEME FOR NONLINEAR PROBLEMS WITH ENGINEERING APPLICATIONS

Abstract

In this study, we offer a novel fractional numerical approach designed to solve nonlinear equations. Based on fractional calculus principles, our technique extends standard numerical methods to account for the fractional-order derivatives found in many real-world occurrences. Analysis of convergence reveals that the order of convergence of the suggested family of approaches is 4 beta + 1 and 8 beta + 4, respectively. We assess the efficacy and convergence qualities of our proposed approach in solving nonlinear equations in various settings using rigorous analysis and numerical experiments. Fractal analysis of the suggested numerical methods for solving nonlinear equations indicates improved convergence behavior and stability than classical methods in the literature.