Existence and uniqueness of global solutions of fractional functional differential equations with bounded delay

This paper deals with initial value problems for fractional functional differential equations with bounded delay. The fractional derivative is defined in the Caputo sense. By using the Schauder fixed point theorem and the properties of the Mittag-Leffler function, new existence and uniqueness results for global solutions of the initial value problems are established. In particular, the unique existence of global solution is proved under the condition close to the Nagumo-type condition.