In some communication systems the transmitted signal is contaminated by impulsive noise with a non-Gaussian distribution. Non-Gaussian noise caused significant performance degradation to communication receivers. The new constant modulus blind equalizer based on fractional lower-order statistics of the equalizer input, referred to as FLOS_CMA, is able to mitigate impulsive channel noise while restoring the constant modulus character of the transmitted communication signal. However, like the constant modulus algorithm (CMA), the steady-state mean square error of the FLOS_CMA algorithm may not be sufficiently low for the system to obtain adequate performance. This paper proposes a concurrent equalizer, in which a decision-directed Least Mean p Norm (DD_LMP) equalizer operates cooperatively with a FLOS_CMA equalizer, controlled through a nonlinear link. Simulation results using M-QAM signaling have shown that the concurrent FLOS_CMA and DD_LMP blind equalizer achieves a dramatic improvement in equalization performance over the FLOS_CMA approach.