Fractional Newton-Raphson Method

Abstract

The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method.

References in corpus (2)

• Reduction of a nonlinear system and its numerical solution using a fractional iterative method
• A nonlinear system related to investment under uncertainty solved using the fractional pseudo-Newton method

Cited by in corpus (10)

• Fractional Newton-Raphson Method Accelerated with Aitken's Method
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• Sets of fractional operators and numerical estimation of the order of convergence of a family of fractional fixed point methods
• Introducción al Cálculo Fraccional
• Reduction of a nonlinear system and its numerical solution using a fractional iterative method
• Acceleration of the order of convergence of a family of fractional fixed point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers
• A nonlinear system related to investment under uncertainty solved using the fractional pseudo-Newton method
• Proposal for Use the Fractional Derivative of Radial Functions in Interpolation Problems
• Numerical solution using radial basis functions for multidimensional fractional partial differential equations of type Black-Scholes
• Fractional flow equations. A model for pressure deficit in an oil well