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

TL;DR

This paper establishes new conditions for the existence and uniqueness of global solutions to fractional functional differential equations with bounded delay, using fixed point theorems and properties of Mittag-Leffler functions.

Contribution

It provides novel existence and uniqueness results for fractional differential equations with bounded delay, extending previous work with new conditions near Nagumo-type criteria.

Findings

Proved existence of global solutions under new conditions.

Established uniqueness of solutions using Schauder fixed point theorem.

Connected solutions to properties of Mittag-Leffler functions.

Abstract

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.