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).
Bucur, C. (2017). Local density of Caputo-stationary functions in the space of smooth functions. ESAIM. COCV, 23(4), 1361-1380 [10.1051/cocv/2016056].
Local density of Caputo-stationary functions in the space of smooth functions
Bucur, C
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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