%0 Journal Article
%T Positive solutions for a nonlocal multi-point boundary-value problem of fractional and second order
%A Ahmed M. A. El-Sayed
%A Ebtisam O. Bin-Taher
%J Electronic Journal of Differential Equations
%D 2013
%I Texas State University
%X In this article we study the existence of positive solutions for the nonlocal multi-point boundary-value problem $$displaylines{ u''(t)+f(t, ^{c}D^{alpha}u(t))=0, quad alpha in(0, 1), ext{ a.e. } tin(0, 1), cr u(0)=0, quad u(1)=sum_{k=1}^m a_k u( au_k), quad au_kin(a, b)subset (0, 1). }$$ We also consider the corresponding integral condition, and the two special cases $alpha = 0 $ and $ alpha = 1$.
%K Fractional calculus
%K boundary value problem
%K nonlocal condition
%K integral condition
%K positive solution
%U http://ejde.math.txstate.edu/Volumes/2013/64/abstr.html