Abstract
In this paper, the authors consider the following fractional high-order three-point boundary value problem: , , , , where , , , , is the standard Riemann-Liouville derivative of order α, and is continuous. By using some fixed point index theorems on a cone for differentiable operators, the authors obtain the existence of positive solutions to the above boundary value problem. MSC:34A08, 34B15.
Highlights
1 Introduction In this paper, we investigate the existence of solutions for the following fractional highorder equation: Dα + u(t) + f t, u(t) =, t ∈ (, )
Differential equations with fractional order are a generalization of the ordinary differential equations to non-integer order
There has been a significant development in the study of fractional differential equations in recent years; see for example [ – ]
Summary
In [ ], using the Guo-Krasnosel’skii fixed point theorem, Goodrich discussed the existence of positive solutions for the following fractional boundary value problem:. Goodrich [ ] investigated the existence of a positive solution to system of fractional boundary value problems and extended his previous study in [ ]. Motivated by the above work of Goodrich, Xu et al [ ] investigated the existence and uniqueness of positive solution for the following fractional boundary value problem:. Different from the literature mentioned above, in the present paper, the authors apply some fixed point theorems for differentiable operators to establish the existence results on positive solutions to the fractional nonlocal boundary value problem
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