Finite time stability of tempered fractional systems with time delays

TL;DR

This paper studies finite time stability of tempered fractional systems with delays, providing sufficient conditions and two approaches for stability analysis, supported by numerical examples.

Contribution

It introduces new stability criteria for tempered fractional systems with delays using H"older, Jensen, and Bellman--Gr"onwall methods.

Findings

Established stability conditions using two different mathematical approaches.

Validated the methods with numerical examples.

Demonstrated the practicality of the stability criteria.

Abstract

We investigate the notion of finite time stability for tempered fractional systems (TFSs) with time delays and variable coefficients. Then, we examine some sufficient conditions that allow concluding the TFSs stability in a finite time interval, which include the nonhomogeneous and the homogeneous delayed cases. We present two different approaches. The first one is based on H\"older's and Jensen's inequalities, while the second one concerns the Bellman--Gr\"onwall method using the tempered Gr\"onwall inequality. Finally, we provide two numerical examples to show the practicability of the developed procedures.