Fractionary iterative methods for solving nonlinear problems

Abstract

In recent years, some point-to-point fractional Newton-type methods have been proposed to find roots of nonlinear equations using fractional derivatives. We present several Newton-type methods based on Caputo fractional derivative. For each case, the order of convergence of the proposed methods is stated, and some numerical tests are carried out in order to observe their performance, in practice. Convergence to different roots depending on the order of the derivative is observed and also differences among the methods in terms of the percentage of converging starting points.