  In this paper, we consider the Cauchy problem for a generalized
parabolic-elliptic Keller-Segel equation with a fractional dissipation and
advection by a weakly mixing (see Definition \ref{def:2.4}). Here the
attractive kernel has strong singularity, namely, the derivative appears in the
nonlinear term by singular integral. Without advection, the solution of
equation blows up in finite time. Under a suitable mixing condition on the
advection, we show the global existence of classical solution with large
initial data in the case of the derivative of dissipative term is higher than
that of nonlinear term. Since the attractive kernel is strong singularity, the
weakly mixing has destabilizing effect in addition to the enhanced dissipation
effect, which makes the problem more complicated and difficult. In this paper,
we establish the $L^\infty$-criterion and obtain the global $L^\infty$ estimate
of the solution through some new ideas and techniques. Combined with
\cite{Shi.2019}, we discuss all cases of generalized Keller-Segel system with
mixing effect, which was proposed by Kiselev, Xu (see \cite{Kiselev.2016}) and
Hopf, Rodrigo (see \cite{Hopf.2018}). Based on more precise estimate of
solution and the resolvent estimate of semigroup operator, we introduce a new
method to study the enhanced dissipation effect of mixing in generalized
parabolic-elliptic Keller-Segel equation with a fractional dissipation. And the
RAGE theorem is no longer needed in our analysis.
