  In this paper, we investigate the existence of solutions for a class of
$p$-Laplacian fractional order Kirchhoff-type system with Riemann-Liouville
fractional derivatives and a parameter $\lambda$. By mountain pass theorem, we
obtain that system has at least one non-trivial weak solution $u_\lambda$ under
some local superquadratic conditions for each given large parameter $\lambda$.
We get a concrete lower bound of the parameter $\lambda$, and then obtain two
estimates of weak solutions $u_\lambda$. We also obtain that $u_\lambda\to 0$
if $\lambda$ tends to $\infty$. Finally, we present an example as an
application of our results.
