This paper deals with active noise control (ANC) for impulsive noise sources for which the filtered-x least mean square (FxLMS) algorithm becomes unstable. By minimizing the fractional lower order moment, the resulting filtered-x least mean p-power (FxLMP) algorithm has an update vector being computed using sign operator and fractional power of the residual error signal. This results in improved robustness as compared with the FxLMS algorithm; however, the convergence speed is very slow. Improvement in convergence speed can be achieved by computing a fractional power for the error as well as for the (filtered) reference signal, combined with efficient normalization of the step-size parameter. This results in filtered-x modified generalized normalized Least mean p-power (FxMGNLMP) algorithm. In this paper we develop a new fractional processing-based adaptive algorithm for ANC of impulsive noise sources. The main idea is to compute a modified update vector for FxMGNLMP algorithm by computing fractional power of the tap-weight vector, and add this update term (after including an appropriate scaling factor) to the original update equation of the FxMGNLMP algorithm. The results of computer simulations demonstrate improved performance of the proposed approach especially when the noise source is highly impulsive.