Uniform asymptotic stability of solutions of fractional functional differential equations

TL;DR

This paper establishes global existence and uniform asymptotic stability results for fractional functional differential equations, extending classical results to fractional orders and highlighting the case when alpha equals 1.

Contribution

It provides new stability and existence results for fractional differential equations, generalizing classical dissipative delay differential equations.

Findings

Proved global existence of solutions.

Established uniform asymptotic stability.

Connected fractional and classical differential equations.

Abstract

In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical dissipative differential equation with delays in [4]