A fractional Traub method with (2α+1)th-order of convergence and its stability

09/19/2019
by   Giro Candelario, et al.
0

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.

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