https://doi.org/10.1140/epjp/s13360-025-06106-5
Regular Article
Prigogine–Resibois master equation with power-law kernel: quantum dynamics with memory
1
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
2
Department of Physics, 915, Moscow Aviation Institute (National Research University), 125993, Moscow, Russia
Received:
27
November
2024
Accepted:
8
February
2025
Published online:
2
April
2025
The Prigogine–Resibois master equations is valid in the general case, regardless of the initial correlations, and make it possible to describe exactly strongly coupled systems. In this paper, exact solutions of the Prigogine–Resibois master equation with power-law kernel (PLK) are derived. To solve this equation we use methods of fractional calculus (FC) and theory of equations with derivatives with non-integer orders. Using the first fundamental theorem of FC, the Prigogine–Resibois master equation with PLK is represented as a fractional differential equation with the Caputo fractional derivative of arbitrary order greater than one. Then, solution of the Cauchy problem with this fractional differential equation is derived. Some properties of these solutions, which are represented via the two-parameter Mittag–Leffler function, are considered. Asymptotic behaviors of the solutions are described.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
