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We analyze the effect of time dependent external field on non-Markovianmigration described by the continuous time random walk (CTRW) approach. Therigorous method of treating the problem is proposed which is based on theMarkovian representations of the CTRW approach and field modulation. The methodis applied to the case of subdiffusive migration in which the exact formulasfor the first and second moments of spatial distribution are derived. Foroscillating external field they predict unusual dependence of the first momenton oscillation phase and anomalous field dependent contribution to

Specific features of the effect of time dependent field on subdiffusing particles. The stochastic Liouville equation approach