摘要：In this paper, we are dedicated to researching the boundary value problems (BVPs) for equation $D^{ lpha }x(t)=f(t,x(t),D^{ lpha -1}x(t))$, with the boundary value conditions to be either: $x(0)=A$, $D^{ lpha -1}x(1)=B$ or $D^{ lpha -1}x(0)=A$, $x(1)=B$. Let the nonlinear term f satisfy some sign conditions, then by making use of the Leray–Schauder nonlinear alternative, some existence results are obtained. In the end, an example is given to verify the main results..
