By defining appropriate Banach space and norm, giving the appropriate projectors , using the coincidence degree theory due to Mawhin and the properties of fractional derivative and integral, the existence of solutions for fractional (n-1,1) conjugate boundary value problems with the Riemann-Stieltjes integral boundary condition at resnonce is investigagted, where the nonlinear term contains fractional-order derivative and may be noncontinuous .An example is given to illustrate the main results.