The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions

In this paper, the existence of solutions for a class of nonlinear boundary value problems of fractional differential equations with integral boundary conditions is studied. Our method is based on the Guo-Krasnoselskii fixed point theorem, allowing us to extend some previously known results. We carefully study the sign of the related Green’s function and get the exact value that it is positive in its domain. The existence of the solution comes from the definition of a suitable cone on a Banach space. Compared with other "positive solutions of nonlinear fractional differential equations with integral boundary value conditions", my main contribution is to generalize the boundary conditions, make them more general, and construct cones cleverly to prove the existence of positive solutions. The conclusion of this paper is illustrated with examples.