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.