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Abstract
Fractional dynamics of open quantum systems with power-law memory is described. We show that the quantum processes can demonstrate a universal dynamic behavior caused by the effects of power-law fading memory. We propose generalizations of time-ordered exponential and time-ordered product for processes with powerlaw memory. As examples, we consider equations of the N-level open quantum system with memory, quantum oscillator with friction and memory. The solutions of the corresponding fractional differential equations with derivatives of noninteger orders are obtained.
