  This article is concerned with the existence and multiplicity of positive
weak solutions for the following fractional Kirchhoff-Choquard problem:
  \begin{equation*}
  \begin{array}{cc}
  \displaystyle M\left( \|u\|^2\right) (-\Delta)^s u = \ds\lambda
f(x)|u|^{q-2}u + \left( \int\limits_{\Omega} \frac{|u(y)|^{2^{*}_{\mu
,s}}}{|x-y|^ \mu}\, dy\right) |u|^{2^{*}_{\mu ,s}-2}u \;\text{in} \; \Omega,
  u > 0\quad \text{in} \; \Omega, \,\,
  u = 0\quad \text{in} \; \mathbb{R}^{N}\backslash\Omega,
  \end{array}
  \end{equation*}
  where $\Omega$ is open bounded domain of $\mathbb{R}^{N}$ with $C^2$
boundary, $N > 2s$ and $s \in (0,1)$, here $M$ models Kirchhoff-type
coefficient of the form $M(t) = a + bt^{\te-1}$, where $a, b > 0$ are given
constants.
  $(-\Delta)^s$ is fractional Laplace operator, $\lambda > 0$ is a real
parameter. We explore using the variational methods, the existence of solution
for ${q} \in (1,2^*_s)$ and $\te \geq 1$.
  % and we also consider the case when $\te > 2^*_{\mu,s}$ for $2< q <
2^*_{s}$.
  Here $2^*_s = \frac{2N}{N-2s}$ and $2^{*}_{\mu ,s} = \frac{2N-\mu}{N-2s}$ is
the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality.
