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.
subdiffusion, fractional derivate, fractional Fokker Planck equation, fractional Hamilton Jacobi Bellman equation, Mean Field Games
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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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1069095
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