  In this paper diffusion processes with changing modes are studied involving
the variable order partial differential equations. We prove the existence and
uniqueness theorem of a solution of the Cauchy problem for fractional variable
order (with respect to the time derivative) pseudo-differential equations.
Depending on the parameters of variable order derivatives short or long range
memories may appear when diffusion modes change. These memory effects are
classified and studied in detail. Processes that have distinctive regimes of
different types of diffusion depending on time are ubiquitous in the nature.
Examples include diffusion in a heterogeneous media and protein movement in
cell biology.
