Advances in Differential Equations

A time-fractional mean field game

Fabio Camilli and Raul De Maio

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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.

Article information

Adv. Differential Equations, Volume 24, Number 9/10 (2019), 531-554.

First available in Project Euclid: 13 August 2019

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Mathematical Reviews number (MathSciNet)

Primary: 35R11: Fractional partial differential equations 60H05: Stochastic integrals 26A33: Fractional derivatives and integrals 40L20 49N70: Differential games


Camilli, Fabio; De Maio, Raul. A time-fractional mean field game. Adv. Differential Equations 24 (2019), no. 9/10, 531--554.

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