Local density of Caputo-stationary functions of any order

Alessandro Carbotti, Serena Dipierro, Enrico Valdinoci

Research output: Contribution to journalArticle

5 Citations (Scopus)
240 Downloads (Pure)

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 ψ-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.

Original languageEnglish
Pages (from-to)1115-1138
Number of pages24
JournalComplex Variables and Elliptic Equations
Volume65
Issue number7
DOIs
Publication statusPublished - 2 Jul 2020

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