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Zbl 1235.34024
Liang, Sihua; Zhang, Jihui
Existence and uniqueness of strictly nondecreasing and positive solution for a fractional three-point boundary value problem.
(English)
[J] Comput. Math. Appl. 62, No. 3, 1333-1340 (2011). ISSN 0898-1221

Summary: We consider the following nonlinear fractional three-point boundary value problem $$\gather D^\alpha_{0+}u(t)+ f(t,u(t))=0,\ 0<t<1,3<\alpha\le 4,\\ u(0)=u'(0)=u''(0)=0, \quad u''(1)=\beta u''(\eta),\endgather$$ where $D^\alpha_{0+}$ is the standard Riemann-Liouville fractional derivative. By using a fixed point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solution to the above boundary value problem.
MSC 2000:
*34A08
34B10 Multipoint boundary value problems
34B18 Positive solutions of nonlinear boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: partially ordered sets; fixed point theorem; positive solution

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