This paper discusses the existence and uniqueness of positive solutions for a periodic boundary value problem of a fractional differential equation in an ordered Banach space E. The existence and uniqueness results of solutions for the associated linear periodic boundary value problem of the fractional differential equation are established, and the norm estimation of resolvent operator is accurately obtained. With the aid of this estimation, the existence and uniqueness results of positive solutions are obtained by using a monotone iterative technique.

In this paper, we are concerned with the periodic boundary value problem of fractional differential equations on ordered Banach spaces. By introducing a concept of upper and lower solutions, we construct a new monotone iterative technique for the periodic boundary value problems of fractional differential equation, and obtain the existence of solutions between lower and upper solutions.

In this paper, we consider the existence of positive solutions for the following boundary value problem of fractional differential equations in Banach spacewhere 0 < α ≤ 1 is real number, I = (0, ω], D α is the Riemann-Liouville fractional derivative, f :Under more general growth and noncompactness measure conditions about nonlinearity f , we obtained the existence of positive solutions by applying the fixed point index theory of condensing mapping.