  Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied,
where the anomalous exponent $\beta(x) \in (0,1)$ varies in space. This type of
situation occurs e.g. in biophysics, where the density of the intracellular
matrix varies throughout a cell. Scaling limits of CTRWs are known to have
probability distributions which solve fractional Fokker-Planck type equations
(FFPE). This correspondence between stochastic processes and FFPE solutions has
many useful extensions e.g. to nonlinear particle interactions and reactions,
but has not yet been sufficiently developed for FFPEs of the"variable order"
type with non-constant $\beta(x)$.
  In this article, variable order FFPEs (VOFFPE) are derived from scaling
limits of CTRWs. The key mathematical tool is the 1-1 correspondence of a CTRW
scaling limit to a bivariate Langevin process, which tracks the cumulative sum
of jumps in one component and the cumulative sum of waiting times in the other.
The spatially varying anomalous exponent is modelled by spatially varying
$\beta(x)$-stable L\'evy noise in the waiting time component. The VOFFPE
displays a spatially heterogeneous temporal scaling behaviour, with generalized
diffusivity and drift coefficients whose units are length$^2$/time$^{\beta(x)}$
resp. length/time$^{\beta(x)}$. A global change of the time scale results in a
spatially varying change in diffusivity and drift.
  A consequence of the mathematical derivation of a VOFFPE from CTRW limits in
this article is that a solution of a VOFFPE can be approximated via Monte Carlo
simulations. Based on such simulations, we are able to confirm that the VOFFPE
is consistent under a change of the global time scale.
