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arXiv · 1809.04005

Local density of Caputo-stationary functions of any order

Alessandro Carbotti·Serena Dipierro·Enrico Valdinoci
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Abstract

We show that any given function can be approximated with arbitrary precision by solutions of linear, time-fractional equations of any prescribed order. This extends a recent result by Claudia Bucur, which was obtained for time-fractional derivatives of order less than one, to the case of any fractional order of differentiation. In addition, our result applies also to the $\psi$-Caputo-stationary case, and it will provide one of the building blocks of a forthcoming paper in which we will establish general approximation results by operators of any order involving anisotropic superpositions of classical, space-fractional and time-fractional diffusions.

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Alessandro Carbotti, Serena Dipierro, Enrico Valdinoci. 2018-09-11. Local density of Caputo-stationary functions of any order. https://arxiv.org/abs/1809.04005

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