Existence of positive solutions for a fractional high-order three-point boundary value problem

被引：0
作者：
Guoqing Chai
Songlin Hu
机构：
[1] Hubei Normal University,College of Mathematics and Statistics
来源：
Advances in Difference Equations | / 2014卷
关键词：
fractional differential equations; three-point boundary value problems; existence results; fixed point index theorem for differentiable operators;
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摘要：
In this paper, the authors consider the following fractional high-order three-point boundary value problem: D0+αu(t)+f(t,u(t))=0, t∈(0,1), u(0)=u′(0)=⋯=u(n−2)(0)=0, D0+α−1u(η)=kD0+α−1u(1), where k>1, η∈(0,1), n−1<α≤n, n≥3, D0+α is the standard Riemann-Liouville derivative of order α, and f:[0,1]×[0,+∞)→[0,+∞) 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.
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[1]  
Xu J(2012)Uniqueness of positive solutions for a class of fractional boundary value problems Appl. Math. Lett 25 590-593
[2]  
Wei Z(2013)Positive solutions of singular fractional equations with integral boundary conditions Math. Comput. Model 57 1053-1059
[3]  
Dong W(2012)A sufficient condition for the existence of a positive solutions for a nonlinear fractional differential equation with the Riemann-Liouville derivative Appl. Math. Lett 25 1986-1992
[4]  
Vong SW(2012)Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations Appl. Math. Lett 25 555-560
[5]  
Yang L(2013)The iterative solutions of nonlinear fractional differential equations Appl. Math. Comput 219 4680-4691
[6]  
Zhang W(2013)A sum operator method for existence and uniqueness of positive solutions to Riemann-Liouville fractional differential equation boundary value problems Commun. Nonlinear Sci. Numer. Simul 18 858-866
[7]  
Liu X(2013)Existence and uniqueness results for boundary value problems of higher order fractional integro-differential equations involving Gronwall’s inequality in Banach spaces Acta Math. Sci 33 758-772
[8]  
Zhang X(2013)Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives Commun. Nonlinear Sci. Numer. Simul 18 2604-2625
[9]  
Han Y(2013)Existence and uniqueness of solutions for impulsive fractional differential equations Appl. Math. Comput 224 422-431
[10]  
Zhang X(2014)Boundary problems for fractional differential equations Appl. Math. Lett 28 14-19
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