摘要：In this paper, we study the existence of solutions for the boundary value problem of the following nonlinear fractional differential equation: D 0 + α [ x ( t ) f ( t , x ( t ) ) ] + g ( t , x ( t ) ) = 0 , 0 < t < 1 , x ( 0 ) = x ( 1 ) = x ′ ( 0 ) = 0 , where 2 < α ≤ 3 is a real number and D 0 + α is the Riemann-Liouville fractional derivative. By a fixed point theorem in Banach algebra, an existence theorem for the boundary value problem of the above fractional differential equation is proved under both Lipschitz and Carathéodory conditions. Two examples are presented to illustrate the main results. MSC:34A08, 34B18.
关键词：fractional differential equation ; boundary value problem ; fractional Green’s function ; fixed point theorem
