On A Nonlinear Fractional Differential Equation On Partially Ordered Metric Spaces

Abstract

In this paper, by using a fixed point result on ordered metric spaces, we prove the existence and uniqueness of a solution of the nonlinear fractional differential equation (, ) via the periodic boundary condition , where and is a continuous increasing function and denotes the Caputo fractional derivative of order alpha. Also, we solve it by using the anti-periodic boundary conditions with and with and separately.