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.


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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