摘要：In this paper, the authors consider the following fractional high-order three-point boundary value problem: D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , t ∈ ( 0 , 1 ) , u ( 0 ) = u ′ ( 0 ) = ⋯ = u ( n − 2 ) ( 0 ) = 0 , D 0 + α − 1 u ( η ) = k D 0 + α − 1 u ( 1 ) , where k > 1 , η ∈ ( 0 , 1 ) , n − 1 < α ≤ n , n ≥ 3 , D 0 + 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. MSC:34A08, 34B15.
关键词：fractional differential equations ; three-point boundary value problems ; existence results ; fixed point index theorem for differentiable operators
