Geodesic
Local density of Caputo-stationary functions in the space of smooth functions
Bucur, Claudia1
1 Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini, 50 20100, Milano Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1361-1380

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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 C k ([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 C k loc (R).

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DOI : 10.1051/cocv/2016056
Classification : 26A33, 34K37, 47G20
Keywords: Caputo stationary, fractional derivative, nonlocal operators

Bucur, Claudia 1

1 Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini, 50 20100, Milano Italy. 
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     title = {Local density of {Caputo-stationary} functions in the space of smooth functions},
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     publisher = {EDP-Sciences},
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Bucur, Claudia. Local density of Caputo-stationary functions in the space of smooth functions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1361-1380. doi: 10.1051/cocv/2016056

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