  In this paper we study continuous time random walks (CTRWs) such that the
holding time in each state has a distribution depending on the state itself.
For such processes, we provide integro-differential (backward and forward)
equations of Volterra type, exhibiting a position dependent convolution kernel.
Particular attention is devoted to the case where the holding times have a
power-law decaying density, whose exponent depends on the state itself, which
leads to variable order fractional equations. A suitable limit yields a
variable order fractional heat equation, which models anomalous diffusions in
heterogeneous media.
