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arXiv · 2001.10846

About Convergence and Order of Convergence of some Fractional Derivatives

Sabrina Roscani·Lucas Venturato
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Abstract

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 $\left|\left| D^{1-\al}f -f'\right|\right|_p$ for p=1 and $p=\infty$ 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.

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Sabrina Roscani, Lucas Venturato. 2020-01-29. About Convergence and Order of Convergence of some Fractional Derivatives. https://arxiv.org/abs/2001.10846

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