Summary: We study the existence of positive solutions for the nonlocal multi-point boundary-value problem \[ \begin{gathered} u''(t)+ f(t,^cD^\alpha u(t))= 0,\quad \alpha\in (0,1),\text{ a.e. }t\in (0,1),\\ u(0)= 0,\quad u(1)= 0,\quad u(1)= \sum^m_{k=1} a_k u(\tau_k),\quad\tau_k\in (a,b)\subset (0,1).\end{gathered} \] We also consider the corresponding integral condition, and the two special cases \(\alpha=0\) and \(\alpha=1\).