  This paper contain a new discussion for the type of generalized nonlinear
Caputo fractional $q$-difference equations with $m$-point boundary value
problem and Riemann-Stieltjes integral
$\tilde{\alpha}[x]:=\int_{0}^{1}~x(t)d\Lambda(t).$ By applying the fixed point
theorem in cones, we investigate an existence of a unique positive solution
depends on $\lambda>0.$ We present some useful properties related to the
Green's function for $m-$point boundary value problem.
