About Convergence and Order of Convergence of some Fractional Derivatives

01/29/2020

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by   Sabrina Roscani, et al.

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In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by || D^1-f -f'||_p for p=1 and p=∞ and we prove that for both Caputo and Caputo Fabrizio operators the order of convergence is a positive real r, 0<r<1. Finally, we compare the speed of convergence between Caputo and Caputo-Fabrizio operators obtaining that they a related by the Digamma function.