Normalized solutions for a critical fractional Choquard equation with a nonlocal perturbation

In this article, we study the fractional critical Choquard equation with a nonlocal perturbation: ( − Δ ) s u = λ u + α ( I μ * ∣ u ∣ q ) ∣ u ∣ q − 2 u + ( I μ * ∣ u ∣ 2 μ , s * ) ∣ u ∣ 2 μ , s * − 2 u , in R N , {\left(-{\Delta })}^{s}u=\lambda u+\alpha \left({I}_{{\mu }^{* }}\hspace{-0.25em}{| u| }^{q}){| u| }^{q-2}u+\left({I}_{{\mu }^{* }}\hspace{-0.25em}{| u| }^{{2}_{\mu ,s}^{* }}){| u| }^{{2}_{\mu ,s}^{* }-2}u,\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N}, having prescribed mass ∫ R N u 2 d x = c 2 , \mathop{\int }\limits_{{{\mathbb{R}}}^{N}}{u}^{2}{\rm