Fractional contact model in the continuum. (English) Zbl 1340.82006

The contact model in the continuum is a model of Markov evolution of a system of interacting particles; see Y. Kondratiev et al. [Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 2, 231–258 (2008; Zbl 1157.60086)]. The authors consider the evolution of the correlation functions in a non-Markov version of the model. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a behavior of time-dependent correlation functions, essentially different from the one known for the standard contact model.


82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
34A08 Fractional ordinary differential equations


Zbl 1157.60086
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