We discuss the existence and uniqueness of solution for two types of fractional order ordinary and delay differential equations. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First we use Banach contraction principle to prove the uniqueness of solution and then Krasnoselskii's fixed point theorem to show the existence of the solution under certain conditions in a Banach space.
"Existence Results for a Class of Fractional Differential Equations with Periodic Boundary Value Conditions and with Delay." Abstr. Appl. Anal. 2013 (SI25) 1 - 8, 2013. https://doi.org/10.1155/2013/176180