# On time-fractional diffusion equations with space-dependent variable order

## TL;DR

This paper studies time-fractional diffusion equations with space-dependent variable order, proving unique determination of the variable order coefficient from boundary measurements, which advances inverse problem theory in fractional PDEs.

## Contribution

It introduces a method to uniquely identify space-dependent variable order coefficients in time-fractional diffusion equations using boundary data.

## Key findings

- Proved well-posedness of the equations.
- Established uniqueness of the variable order coefficient from boundary measurements.
- Contributed to inverse problems in fractional PDEs.

## Abstract

We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other coefficients of these equations, by the knowledge of a suitable time-sequence of partial Dirichlet-to-Neumann maps.