Well-Posedness of a Fractional Mean Field Game System with Non-Local Coupling

Abstract

We prove existence and uniqueness of classical solutions for a fractional Mean Field Game system with non-local coupling, where the fractional exponent is greater than 1/2. To our knowledge this is not proven before in the literature, and is therefore a new result. In addition, we show regularity in time and space for the fractional Hamilton- Jacobi equation, and use this result to show regularity for the fractional Fokker-Planck equation.