  In this paper, we consider an aggregation equation with fractional diffusion
and large shear flow, which arise from modelling chemotaxis in bacteria.
Without the advection, the solution of aggregation equation may blow up in
finite time. First, we study the enhanced dissipation of shear flow by
resolvent estimate method, where the fractional Laplacian
$(-\Delta)^{\alpha/2}$ is considered and $\alpha\in (0,2)$. Next, we show that
the enhanced dissipation of shear flow can suppress blow-up of solution to
aggregation equation with fractional diffusion and establish global classical
solution in the case of $\alpha\geq 3/2$. Here we develop some new technical to
overcome the difficult of low regularity for fractional Laplacian.
