About Convergence and Order of Convergence of Some Fractional Derivatives

ROSCANI, SABRINA D.; VENTURATO, LUCAS D.

Progress in Fractional Differentiation and Applications

Natural Science Publishing

Año: 2022 vol. 8 p. 495 - 508

2356-9336

In this paper we obtain some convergence results for Riemann-Liouville, Caputo, and Caputo--Fabrizio fractional operators when the order of differentiation approaches one. We consider the errors given by $|| D^{1-\al}f -f'||_p$ for p=1 and $p=\infty$ and we prove that for bothm the Caputo and Caputo Fabrizio operators, the order of convergence is a positive real $r \in (0,1)$. Finally, we compare the speed of convergence between Caputo and Caputo--Fabrizio operators obtaining that they are related by the Digamma function.