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A time-fractional mean field game. (English) Zbl 1442.35502
Summary: We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and the Fokker-Planck equations. We discuss separately the well-posedness for each of the two equations and then we prove existence and uniqueness of the solution to the Mean Field Games system.

MSC:
35R11 Fractional partial differential equations
49L20 Dynamic programming in optimal control and differential games
49N80 Mean field games and control
60H05 Stochastic integrals
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Full Text: Euclid