Abstract:

The paper is concerned with the existence of solutions for a class of fractional differential equations boundary value problems with Caputo derivative, where there exist fractional derivative in the boundary conditions and the nonlinear term  f:［0,1］×［0,∞)→［0,∞) satisfies Caratheodory conditions.By using the Krasnosel’skii fixed theorem on a cone, the sufficient conditions for the problem at least one and two positive solutions are obtained.

Key words: positive solutions; Caputo derivative; boundary value problems; fixed point theorem