Advances in Differential Equations
- Adv. Differential Equations
- Volume 24, Number 9/10 (2019), 531-554.
A time-fractional mean field game
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.
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)
Camilli, Fabio; De Maio, Raul. A time-fractional mean field game. Adv. Differential Equations 24 (2019), no. 9/10, 531--554. https://projecteuclid.org/euclid.ade/1565661669