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).
Local density of Caputo-stationary functions in the space of smooth functions / C. Bucur. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - 23:4(2017 Oct), pp. 1361-1380.
Local density of Caputo-stationary functions in the space of smooth functions
C. BucurPrimo
2017
Abstract
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).
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