The influence of an external varying field on the non-Markovian migration of particles described in the continuous-time random walk model (CTRWM) was analyzed theoretically. In terms of the Markovian representation for the CTRWM suggested earlier, a rigorous method for describing the influence of an external force was developed. This method reduced the problem to solving the non-Markovian stochastic Liouville equation (SLE) for the particle distribution function. An analysis of the derived SLE and its comparison with the earlier equations were performed. The method was used to study the characteristic features of the time dependence of the first and second moments of the distribution function for particles involved in subdiffusion motion in a uniform varying external field. Both oscillating and fluctuating fields were considered. In both cases, anomalously strong field effects on the second particle distribution moment (variance) were observed. This influence was especially strong for a fluctuating field, and in the limit of anomalously slow fluctuations at that.
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