The dynamical analysis of a low computational cost family of higher-order fractional iterative method

Abstract

Fractional calculus has been more important in many fields of science and engineering in recent years. It has developed into an engaging and productive area of mathematical research. In this article, our goal is to investigate how these derivatives with fractional orders affect how close nonlinear equations zeros $\tilde{y}$ are to being true. The present work examines the higher-order family of iterative techniques that use Caputo and Conformable fractional derivatives of at least cubic order to identify the roots of a nonlinear equations. Moreover, the higher-order Conformable fractional iterative methods perform better when the order of derivative lies $0<\beta \le \frac{1}{2}$.

Keywords:

• Caputo's fractional derivative
• conformable fractional derivatives
• nonlinear equation
• and $\mathcal{K}$-type method
• convergence plane

AMS SUBJECT CLASSIFICATIONS:

• 65H105
• 26A33

Disclosure statement

No potential conflict of interest was reported by the author(s).