Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems

In this paper we establish the existence of at least two (weak) solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearities\begin{document}$\begin{cases}M\left(\|u\|^{{n}/{s}}\right)(-\Delta)^s_{n/s}u = \mu u^{-q}+ u^{r-1}\exp( u^{\beta})\quad\text{in } \Omega,\\u>0\qquad\text{in } \Omega,\\u = 0\qquad\text{in } \mathbb R^n \setminus{ \Omega}, \end{cases} $\end{document}where \begin{document}$ \Omega $\end{document} is a smooth bounded domain of \begin{document}$ \mathbb R^n $\end{document} , \begin{document}$ n\geq 1 $\end{document} , \begin{document}$ s\in (0,1) $\end{document} , \begin{document}$ \mu>0 $\end{document} is a real parameter, \begin{document}$ \beta <{n/(n-s)} $\end{document} and \begin{document}$ q\in (0,1) $\end{document} .The paper covers the so called degenerate Kirchhoff case andthe existence proofs rely on the Nehari manifold techniques.