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

In this paper, we study the following class of fractional Choquard-type equations $$\begin{aligned} (-\Delta )^{1/2}u + u=\Big ( I_\mu *F(u)\Big )f(u), \quad x\in \mathbb {R}, \end{aligned}$$ where $$(-\Delta )^{1/2}$$ denotes 1/2-Laplacian operator, $$I_{\mu }$$ is Riesz potential with $$0<\mu <1$$ , and F primitive function f. We use variational methods minimax estimates to existence solutions when f has critical exponential growth in sense Trudinger–Moser inequality.