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Modeling of crowds of pedestrians has been considered in this paper fromdifferent aspects. Based on fractional microscopic model that may be much moreclose to reality, a fractional macroscopic model has been proposed usingconservation law of mass. Then in order to characterize the competitive andcooperative interactions among pedestrians, fractional mean field games areutilized in the modeling problem when the number of pedestrians goes toinfinity and fractional dynamic model composed of fractional backward andfractional forward equations are constructed in macro scale. Fractionalmicro-macro model for crowds of pedestrians are obtained in the end. Simulationresults are also included to illustrate the proposed fractional microscopicmodel and fractional macroscopic model respectively.

A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games