ASYMPTOTIC DYNAMICS OF NON-AUTONOMOUS FRACTIONAL REACTION-DIFFUSION EQUATIONS ON BOUNDED DOMAINS

In this paper, we consider the asymptotic dynamics of nonautonomous fractional reaction-diffusion equations of the form u(i )+ (-Delta)(8)u + f(u) = g(t) complemented with the Dirichlet boundary condition on a bounded domain. First, we obtain some higher-attraction results for pullback attractors, that is, without any additional t-differentiability assumption on the forcing term g, for any space dimension N and any growth power p >= 2 of f, the known (L-2 (Omega), L-2 (Omega)) pullback attractor can indeed attract every L-2 (Omega)-bounded set in the L2+delta (Omega)-norm for every delta is an element of [0, infinity) as well as in the Wo8,2 (Omega)-norm. Then, we construct a family of Borel probability measures {mu(t)}t is an element of R, whose supports satisfy the higher-attraction results. Finally, we investigate the relationship between such the Borel probability measures and time-dependent statistical solutions for this fractional Laplacian equation.