This paper is concerned with the long time behavior of solutions for a non-autonomous reaction-diffusion equations with anomalous diffusion. Under suitable assumptions on nonlinearity and external force, the global well-posedness has been studied. Then the pullback attractors in and () have been achieved with a restriction on the growth order of nonlinearity as . The results presented can be seen as the extension for classical theory of infinite dimensional dynamical system to the fractional diffusion equations.
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