Well-Posedness of a Fractional Mean Field Game System with Non-Local Coupling
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We prove existence and uniqueness of classical solutions for a fractional Mean FieldGame system with non-local coupling, where the fractional exponent is greater than1/2. To our knowledge this is not proven before in the literature, and is therefore a newresult. 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-Planckequation.