Normalized solutions for a fractional Choquard-type equation with exponential critical growth in $\mathbb{R}$

In this paper, we study the following fractional Choquard-type equation with prescribed mass \begin{align*} \begin{cases} (-Δ)^{1/2}u=λu +(I_μF(u))f(u),\ \ \mbox{in}\ $\mathbb{R}$, \displaystyle\int_{$\mathbb{R}$}|u|^2 $\mathrm{d}$x=a^2, \end{cases} \end{align} where $(-\mathrm{\Delta }{)}^{1\mathrm{/}2}$ denotes the $1\mathrm{/}2$-Laplacian operator, $a>0$, $\lambda \in \mathbb{R}$, $I_{\mu }(x)=\frac{1}{\mathrm{\mid }x{\mathrm{\mid }}^{\mu }}$ with $\mu \in (0,1)$, $F(u)$ is the primitive function of $f(u)$, and $f$ is a continuous function with exponential critical growth in the sense of the Trudinger-Moser inequality. By using a minimax principle based on the homotopy stable family, we obtain that there is at least one normalized ground state solution to the above equation.