Strong Solution for Fractional Mean Field Games with Non-Separable Hamiltonians

Abstract

In this paper, we establish the existence and uniqueness of a strong solution to a fractional mean field games system with non-separable Hamiltonians, where the fractional exponent σ∈(12,1). Our result is new for fractional mean field games with non-separable Hamiltonians, which generalizes the work of D.M. Ambrose for the integral case. The important step is to choose the new appropriate fractional order function spaces and use the Banach fixed-point theorem under stronger assumptions for the Hamiltonians.