摘要：In this paper, we study the uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = 0 , u ( 1 ) = a D α − 1 2 u ( t ) t = ξ , where 1 < α ≤ 2 is a real number, D 0 + α is the standard Riemann-Liouville differentiation and f : ( 0 , 1 ] × [ 0 , + ∞ ) → [ 0 , + ∞ ) , with lim t → 0 + f ( t , ⋅ ) = + ∞ . Our analysis relies on a fixed-point theorem in partially ordered set. As an application, an example is presented to illustrate the main result. MSC:26A33, 34B15, 34K37.
关键词：boundary value problem ; singular fractional differential equations ; Riemann-Liouville fractional derivative ; uniqueness ; partially ordered set
