FTS and FTB of Conformable Fractional Order Linear Systems

Abstract

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

Consensus of linear conformable fractional order multi‐agent systems with impulsive control protocols

“…Subsequently, the conformable fractional derivative is extended to more general case by Zhao and Luo; meanwhile, its physical background is illustrated [33]. Some results about finite-time stability and boundedness related to conformable fractional order linear systems are studied in Ben Makhlouf et al [34]. Souahi studies stability of conformable fractional order nonlinear systems in Souahi et al [35].…”

Stability Analysis of COVID-19 Epidemic Model of Type S E I Q H R with Fractional Order

“…Subsequently, Abdeljawad [25] developed the properties of the conformable fractional derivative. After that, Benmakhlouf et al [26] studied the finite time stability (FTS) and finite time boundedness (FTB) of the conformable fractional derivative. Currently, Hattaf [27,28] introduced a new definition of the fractional derivative with a non-singular kernel in the sense of Caputo to generalize the various types by making these properties, and he proposed an approach for studying the stability of the latter.…”

Improved Quasiuniform Stability for Fractional Order Neural Nets with Mixed Delay

“…Note that the fractional-order calculus has been used in studying the systems' dynamics in many fields such as electrochemistry, physics, viscoelasticity, biology, and chaotic systems [1]. In a related context, the evolution of science and engineering systems has considerably stimulated the employment of the fractional calculus in many areas of the control theory, in the last decades, and this includes stability [3][4][5][6], finite-time stability (FTS) [7][8][9], stabilization [10], observer design [10,11], and fault estimation [12][13][14].…”