On the regularity of the attractor for a new class of fractional nonlinear Klein–Gordon–Schrödinger systems

The main goal of this paper is to study the asymptotic behavior of a weakly damped forced fractional nonlinear Klein–Gordon–Schrödinger system in one dimensional unbounded domain. We prove the existence of a global attractor $$\mathcal {A}_{\alpha }\; \left( \alpha \in (\frac{1}{2},1)\right) $$ of the systems of the fractional nonlinear Klein–Gordon–Schrödinger (FNLKGS) equations in $$H^{\alpha }(\mathbb {R})\times H^{\alpha }(\mathbb {R})\times L^2(\mathbb {R})$$ and more particularly that this attractor is in fact a compact set of $$H^{2\alpha }(\mathbb {R})\times H^{2\alpha }(\mathbb {R})\times H^{\alpha }(\mathbb {R})$$ .