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Featured Application: The method can be applied to active noise control (ANC). As all actual environments are unknown, the tap-length considerably influences ANC. The proposed algorithm can determine the optimal tap-length to optimize computation time and avoid the under-modeling problem. The effect of noise reduction can be improved to a certain extent. Convergence speed and steady-state performance are important factors to estimate the variable tap-length algorithm. The step-size of tap-length (ST) and the error width considerably impact the performance of the fractional variable tap-length algorithm. A mixed fractional variable tap-length algorithm that simultaneously applies time-varying ST and error width strategies is presented in this paper. The ST and the error width are analyzed in detail. This method uses the same variable to control both aspects, so their changes are relatively consistent. The parameters have strong adaptive ability at different stages. The proposed algorithm can solve some defects of the previous algorithms, including slow convergence rate, weak steady-state performance and robustness. A novel mean square deviation (MSD) gradient experiment is performed. Experimental results show good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]