Initial value problems for arbitrary order fractional differential equations with delay

By fixed point theory the nonlinear alternative of Leray–Schauder type, and the properties of absolutely continuous functions space, we study the existence and uniqueness of initial value problems for nonlinear higher fractional equations with delay, and obtain some new results involving local and global solutions.

•The authors gave existence results of IVP for arbitrary order fractional differential equations with delay.•And then, they came to a uniqueness theorem that corresponds to Picard–Lindelöf result.•Moreover, they explored other sufficient conditions for existence and uniqueness.•In fact, they derived a global existence and uniqueness result for a large class of equation.