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In this article, we discuss the existence and uniqueness of solution to fractional order ordinary and delay differential equations. We apply our results on the single species model of Lotka Volterra type. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First we use Banach contraction principle and then Krasnoselskii's fixed point theorem to show the existence and uniqueness of the solution under certain conditions. Moreover, we prove that the solution can be extended to maximal interval of existence.