Asymptotic method of moving planes for fractional parabolic equations

In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties positive solutions for fractional parabolic equations. We first obtain series needed key ingredients such as narrow region principles, and various maximum strong principles antisymmetric functions both bounded unbounded domains. Then illustrate how new can be employed radial symmetry monotonicity unit ball on the whole space. Namely, show that no matter what initial data are, will eventually radially symmetric functions. firmly believe ideas methods introduced here conveniently applied study variety nonlocal problems with more general operators nonlinearities.