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

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 $C^k([0,1])$ function can be approximated in $[0,1]$ by a a function that is Caputo-stationary in $[0,1]$, with initial point $a<0$. Otherwise said, Caputo-stationary functions are dense in $C_{loc}^k(\mathbb{R})$.

19 pages, 4 figures

References in corpus (1)

• Nonlocal diffusion and applications

Cited by in corpus (4)

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• Weyl and Marchaud derivatives: a forgotten history