Wellposedness and smoothing properties of history-state-based variable-order time-fractional diffusion equations (Q2300672)

The main aim of this paper is to provide new theorems on the well-posedness and regularity properties of history-state-based variable-order time-fractional diffusion equations in multiple space dimensions. The paper is organised as follows: following preliminaries, the authors consider modelling issues and give some results to be used later. They prove lifting properties of the variable-order fractional integral operators and go on to prove well-posedness and regularity properties of variable-order ordinary differential equations. This provides the necessary basis for analysis of the history-state-based variable-order time-fractional diffusion equations.