Inserted: 21 mar 2020
Journal: Complex Variables and Elliptic Equations
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