  Based on the nonincreasing property of quantum coherence via skew information
under incoherent completely positive and trace-preserving maps, we propose a
non-Markovianity measure for open quantum processes. As applications, by
applying the proposed measure to some typical noisy channels, we find that it
is equivalent to the three previous measures of non-Markovianity for phase
damping and amplitude damping channels, i.e., the measures based on the quantum
trace distance, dynamical divisibility, and quantum mutual information. For the
random unitary channel, it is equivalent to the non-Markovianity measure based
on $l_1$ norm of coherence for a class of output states and it is incompletely
equivalent to the measure based on dynamical divisibility. We also use the
modified Tsallis relative $\alpha$ entropy of coherence to detect the
non-Markovianity of dynamics of quantum open systems, the results show that the
modified Tsallis relative $\alpha$ entropy of coherence are more comfortable
than the original Tsallis relative $\alpha$ entropy of coherence for small
$\alpha$.
