A fractional Traub method with $(2α+1)$th-order of convergence and its stability
Some fractional Newton methods have been proposed in order to find roots of nonlinear equations using fractional derivatives. In this paper we introduce a fractional Newton method with order $α+1$ and compare with another fractional Newton method with order $2α$. We also introduce a fractional Traub method with order $2α+1$ and compare with its first step (fractional Newton method with order $α+1$). Some tests and analysis of the dependence on the initial estimations are made for each case.
math.NA↗