Finite time stability of tempered fractional systems with time delays

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 Hölder's and Jensen's inequalities, while the second one concerns the Bellman--Grönwall method using the tempered Grönwall inequality. Finally, we provide two numerical examples to show the practicability of the developed procedures.

This is a preprint version of the paper published open access in 'Chaos Solitons Fractals'

References in corpus (2)

• On some analytic properties of tempered fractional calculus
• On tempered fractional calculus with respect to functions and the associated fractional differential equations

Cited by in corpus (1)

• Controllability and observability of tempered fractional differential systems