摘要：By using fixed point results on cones, we study the existence of solutions for the singular nonlinear fractional boundary value problem D α c u ( t ) = f ( t , u ( t ) , u ′ ( t ) , c D β u ( t ) ) , u ( 0 ) = a u ( 1 ) , u ′ ( 0 ) = b c D β u ( 1 ) , u ″ ( 0 ) = u ‴ ( 0 ) = u ( n − 1 ) ( 0 ) = 0 , where n ≥ 3 is an integer, α ∈ ( n − 1 , n ) , 0 1 α − 1 and f ( t , x , y , z ) may be singular at value 0 in one dimension of its space variables x, y, z. Here, c D stands for the Caputo fractional derivative.
关键词：boundary value problem ; fixed point ; fractional differential equation ; Green function ; regularization ; singular
