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About Convergence and Order of Convergence of Some Fractional Derivatives |
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PP: 495-508 |
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doi:10.18576/pfda/080404
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Author(s) |
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Sabrina Dina Roscani,
Lucas David Venturato,
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Abstract |
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| 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.
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