Existence of positive solutions for boundary value problems of fractional functional differential equations. (English) Zbl 1213.34093
Summary: This paper deals with the existence of positive solutions for the boundary value problem involving a nonlinear functional differential equation of fractional order \(\alpha\) given by
\[ D^{\alpha} u(t) + f(t, u_t) = 0, t \in (0, 1),\quad 2 < \alpha \leq 3, \]
\[ u'(0) = 0, u'(1) = b u'(\eta),\quad u_0 = \phi. \]
Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel’skii’s fixed point theorem.
\[ D^{\alpha} u(t) + f(t, u_t) = 0, t \in (0, 1),\quad 2 < \alpha \leq 3, \]
\[ u'(0) = 0, u'(1) = b u'(\eta),\quad u_0 = \phi. \]
Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel’skii’s fixed point theorem.
MSC:
| 34K37 | Functional-differential equations with fractional derivatives |
| 47N20 | Applications of operator theory to differential and integral equations |
| 34K10 | Boundary value problems for functional-differential equations |
