These notes are an introduction to Mean Field Game (MFG) theory, which models differential
games involving infinitely many interacting players. We focus here on the Partial Differential …

A time-fractional mean-field control (MFC) is developed for a prototype model of accidental
spill of a hazardous contaminant in subsurface porous media, which is a representative and …

Abstract We study Mean Field Games (MFGs) driven by a large class of nonlocal, fractional
and anomalous diffusions in the whole space. These non-Gaussian diffusions are pure jump …

We study existence, uniqueness and regularity properties of classical solutions to viscous
Hamilton–Jacobi equations with Caputo time-fractional derivative. Our study relies on a …

A mean field game model in the interpretation of optimal control is investigated theoretically
and numerically. This is the problem of minimizing a non-convex and non-coercive objective …

In this paper, we study the numerical approximation of a system of PDEs with fractional time
derivatives. This system is derived from an optimal control problem for a time-fractional …

We consider an optimal control problem of an advection-diffusion equation with Caputo time-
fractional derivative. By convex duality method we obtain as optimality condition a forward …

We introduce a class of fully nonlinear mean field games posed in. We justify that they are
related to controlled local or nonlocal diffusions, and more generally in our setting, to a new …

In this work, we investigate a variational formulation for a time-fractional Fokker-Planck
equation which arises in the study of complex physical systems involving anomalously slow …

We consider the variational structure of a time-fractional second-order mean field games
(MFG) system. The MFG system consists of time-fractional Fokker–Planck and Hamilton …