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 frac- tional 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.
A time-fractional mean field game / Camilli, Fabio; DE MAIO, Raul. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 9/10:24(2019), pp. 531-554.
A time-fractional mean field game
Fabio Camilli;Raul De Maio
2019
Abstract
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 frac- tional 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.File allegati a questo prodotto
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