Volume 23, Number 4, October-December 2017
|Page(s)||1361 - 1380|
|Published online||21 June 2017|
Local density of Caputo-stationary functions in the space of smooth functions∗
Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini, 50 20100, Milano Italy.
Received: 30 June 2015
Revised: 9 May 2016
Accepted: 8 August 2016
We consider the Caputo fractional derivative and say that a function is Caputo-stationary if its Caputo derivative is zero. We then prove that any Ck( [ 0,1 ]) function can be approximated in [0,1] by a function that is Caputo-stationary in [0,1], with initial point a< 0. Otherwise said, Caputo-stationary functions are dense in Ckloc(R).
Mathematics Subject Classification: 26A33 / 34K37 / 47G20
Key words: Caputo stationary / fractional derivative / nonlocal operators
© EDP Sciences, SMAI 2017
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