Homogenization of parabolic problems for non-local convolution type operators under non-diffusive scaling of coefficients

We study homogenization problem for non-autonomous parabolic equations of the form ${\mathrm{\partial }}_{t}u=L(t)u$ with an integral convolution type operator $L(t)$ that has a non-symmetric jump kernel which is periodic in spatial variables and in time. It is assumed that the space-time scaling of the environment is not diffusive. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled, and the homogenization result holds in a moving frame.