## About Convergence and Order of Convergence of some Fractional Derivatives

29 Jan 2020  ·  Roscani Sabrina, Venturato Lucas ·

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. read more

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Analysis of PDEs Numerical Analysis Classical Analysis and ODEs Numerical Analysis