A Conformable Fractional Weerakoon-Fernando Method for Solving Nonlinear Equations and Its Generalization for Nonlinear Systems

Abstract

This study introduces a new conformable Weerakoon-Fernando method designed to solve nonlinear equations, the classical Weerakoon-Fernando method is a special case of the conformable Weerakoon-Fernando method. In addition, the proposed method has been extended to its multi-dimensional version, enabling it to effec tively solve systems of nonlinear equations. Moreover, we present a comprehensive analysis of convergence for the proposed methods. Through numerical comparisons, we highlight the substantial improvements in both convergence rate and accuracy offered by these methods. Furthermore, the convergence planes generated by the proposed methods demonstrate strong stability and a significantly
higher convergence percentage.