Positive solutions for periodic boundary value problem of fractional differential equation in Banach spaces

Abstract

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.

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