Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 64, pp. 1-8.
Title: Positive solutions for a nonlocal multi-point boundary-value problem
of fractional and second order
Authors: Ahmed M. A. El-Sayed (Alexandria Univ., Alexandria, Egypt)
Ebtisam O. Bin-Taher (Alexandria Univ., Alexandria, Egypt)
Abstract:
In this article we study the existence of positive solutions for
the nonlocal multi-point boundary-value problem
$$\displaylines{
u''(t)+f(t, ^{c}D^{\alpha}u(t))=0, \quad \alpha \in(0, 1), \text{ a.e. }
t\in(0, 1), \cr
u(0)=0, \quad u(1)=\sum_{k=1}^m a_k u(\tau_k), \quad
\tau_k\in(a, b)\subset (0, 1).
}$$
We also consider the corresponding integral condition, and the
two special cases $\alpha = 0 $ and $ \alpha = 1$.
Submitted March 19, 2012. Published March 05, 2013.
Math Subject Classifications: 34B10, 26A33
Key Words: Fractional calculus; boundary value problem; nonlocal condition;
integral condition; positive solution.