Calculus of Variations and Geometric Measure Theory

A. Carbotti - S. Dipierro - E. Valdinoci

Local density of Caputo-stationary functions of any order

created by carbotti on 21 Mar 2020


Published Paper

Inserted: 21 mar 2020

Journal: Complex Variables and Elliptic Equations
Pages: 24
Year: 2018
Doi: 10.1080/17476933.2018.1544631

ArXiv: 1809.04005 PDF


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 subsequent work in which we will establish general approximation results by operators of any order involving anisotropic superpositions of classical, space-fractional and time-fractional diffusions.

Keywords: Density results; approximation; Caputo derivative; higher order operators