A study on the use of conformable fractional derivativesin the Newton-Raphson Method

Abstract

This paper investigates the application of conformable fractional derivatives to iterative methods for finding the roots of nonlinear equations. We review the definition of the conformable fractional derivative and its generalization. Motivated by this framework, we introduce two perturbation functions, e(α−1)x and e(1−α)x, with α ∈ (0,1], and incorporate them into a Newton–Raphson-type scheme. A theoretical analysis establishing local linear convergence is presented, together with numerical experiments implemented in Python. The proposed approach is evaluated on quadratic and cubic polynomials by comparing the two perturbation functions. The results indicate that, for suitable values of α, the proposed method may converge in fewer iterations than the classical Newton Raphson method and can even converge in situations where the classical method fails.