  We study a simple nonlocal-in-time dynamic system proposed for the effective
modeling of complex diffusive regimes in heterogeneous media. We present its
solutions and their commonly studied statistics such as the mean square
distance. This interesting model employs a nonlocal operator to replace the
conventional first-order time-derivative. It introduces a finite memory effect
of a constant length encoded through a kernel function. The nonlocal-in-time
operator is related to fractional time derivatives that rely on the entire
time-history on one hand, while reduces to, on the other hand, the classical
time derivative if the length of the memory window diminishes. This allows us
to demonstrate the effectiveness of the nonlocal-in-time model in capturing the
crossover widely observed in nature between the initial sub-diffusion and the
long time normal diffusion.
