In this paper, some applications of ordered version of fixed point theorems to differential equation is illustrated. The existence of fixed point in partially ordered sets endowed with a metric was investigated by Ran and Reurings [1] and then by Nieto and Lopez [2]. I this paper, we establish some results in fixed point theorem for such contractions in ordered cone metric spaces without assuming the normality of cone. These are the extended results of Presic[3] and Ciric and Presic[4] in ordered cone metric spaces. We also prove some fixed point theorems for  -Ciric-Presic type contractions. We also generate and extend the Banach Contraction Principle and several known result in product spaces when the underlying space is an ordered cone metric space. Some examples to illustrate the results are also given in the end.