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Xu, Yufeng; He, Zhimin

Existence of solutions for nonlinear high-order fractional boundary value problem with integral boundary condition. (English) Zbl 1296.34042

J. Appl. Math. Comput. 44, No. 1-2, 417-435 (2014).
Summary: The main purpose of this paper is to present the existence results of solutions and positive solutions of nonlinear high-order fractional boundary value problems with integral boundary condition. By using the Banach fixed point theorem and the Krasnosel’skii fixed point theorem, we obtain the existence and uniqueness of real solution. By the Guo-Krasnosel’skii fixed point theorem on the cone, we obtain a desired result for guaranteeing the existence of positive solution. Several interesting examples relevant to the main results are also considered.

Cited in 4 Documents

MSC:

34A08 Fractional ordinary differential equations
47H10 Fixed-point theorems

Keywords:

fractional differential equations; boundary value problem; fractional calculus; fixed point theorem; positive solution
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References:

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