Progress in Fractional Differentiation & Applications
Abstract
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 D1−α f − f ′p for p=1 and p = ∞ and we prove that for bothm the Caputo and Caputo Fabrizio operators, the order of convergence is a positive real r ∈ (0, 1). Finally, we compare the speed of convergence between Caputo and Caputo–Fabrizio operators obtaining that they are related by the Digamma function.
Digital Object Identifier (DOI)
http://dx.doi.org/10.18576/pfda/080404
Recommended Citation
Dina Roscani, Sabrina and David Venturato, Lucas
(2022)
"About Convergence and Order of Convergence of Some Fractional Derivatives,"
Progress in Fractional Differentiation & Applications: Vol. 8:
Iss.
4, Article 4.
DOI: http://dx.doi.org/10.18576/pfda/080404
Available at:
https://digitalcommons.aaru.edu.jo/pfda/vol8/iss4/4