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We consider the Caputo fractional derivative and say that a function isCaputo-stationary if its Caputo derivative is zero. We then prove that any$C^k\big([0,1]\big)$ function can be approximated in $[0,1]$ by a a functionthat is Caputo-stationary in $[0,1]$, with initial point $a<0$. Otherwise said,Caputo-stationary functions are dense in $C^k_{loc}(\mathbb{R})$.

Local density of Caputo-stationary functions in the space of smooth functions