New criteria for finite-time stability of nonlinear fractional-order delay systems: A Gronwall inequality approach

Phát, Vũ Ngọc; Thành, Nguyễn Trường

doi:10.1016/j.aml.2018.03.023

Cited by 66 publications

(39 citation statements)

References 11 publications

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“…For example, in Ref [29], V.N. Phat et al discussed the finite time stability of nonlinear fractional order system by means of Gronwall inequality approach.…”

Section: Introductionmentioning

confidence: 99%

Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

Anbalagan

Raja

Rajchakit

et al. 2019

Adaptive Control & Signal

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Item Type Article Authors Pratap, A.; Dianavinnarasi, J.; Raja, R.; Rajchakit, G.; Cao, J.; Bagdasar, Ovidiu Citation Rajchakit, G., et al (2019) 'Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays'. AbstractThis paper deals with the extended design of Mittag-Leffler state estimator and adaptive synchronization for fractional order BAM neural networks (FBNNs) with time delays. By the aid of Lyapunov direct approach and Razumikhin-type method a suitable fractional order Lyapunov functional is constructed and a new set of novel sufficient condition are derived to estimate the neuron states via available output measurements such that the ensuring estimator error system is globally Mittag-Leffler stable. Then, the adaptive feedback control rule is designed, under which the considered FBNNs can achieve Mittag-Leffler adaptive synchronization by means of some fractional order inequality techniques. Moreover, the adaptive feedback control may be utilized even when there is no ideal information from the system parameters. Finally, two numerical simulations are given to reveal the effectiveness of the theoretical consequences.

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“…For example, in Ref [29], V.N. Phat et al discussed the finite time stability of nonlinear fractional order system by means of Gronwall inequality approach.…”

Section: Introductionmentioning

confidence: 99%

Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

Anbalagan

Raja

Rajchakit

et al. 2019

Adaptive Control & Signal

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“…Moreover, some attractiveness results for fractional functional differential equations were obtained in using a fixed‐point theorem. Finally, a robust finite‐time stability problem of fractional‐order systems with time‐varying delay and nonlinear perturbation was investigated in based on a generalized Gronwall inequality. A delay‐dependent sufficient condition for robust finite‐time stability of such systems was provided there in terms of the Mittag–Leffler function.…”

Section: Introductionmentioning

confidence: 99%

Convergence and stability estimates in difference setting for time‐fractional parabolic equations with functional delay

Hendy

Пименов

Macías‐Díaz

2019

Numerical Methods Partial

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A class of one‐dimensional time‐fractional parabolic differential equations with delay effects of functional type in the time component is numerically investigated in this work. To that end, a compact difference scheme is constructed for the numerical solution of those equations based on the idea of separating the current state and the prehistory function. In these terms, the prehistory function is approximated by means of an appropriate interpolation–extrapolation operator. A discrete form of the fractional Gronwall inequality is employed to provide an optimal error estimate. The existence and uniqueness of the numerical solutions, the order of approximation error for the constructed scheme, the stability and the order of convergence are mathematically investigated in this work.

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“…In this paper, we mainly study the finitetime stability, which has been investigated by some researchers. For an extensive collection of such results, we refer the readers to the related literatures, such as the papers [19][20][21][22][23]. In detail, in [19], Wu et al studied the finite-time stability of Caputo delta fractional linear difference equations with the aid of Grönwall inequality.…”

Section: Introductionmentioning

confidence: 99%

“…Phat and anh [22] considered the following nonlinear FOSs with time-varying delay and nonlinear disturbance:…”

Section: Introductionmentioning

confidence: 99%

On the Novel Finite-Time Stability Results for Uncertain Fractional Delay Differential Equations Involving Noninstantaneous Impulses

Luo

et al. 2019

Mathematical Problems in Engineering

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New criteria for finite-time stability of nonlinear fractional-order delay systems: A Gronwall inequality approach

Cited by 66 publications

References 11 publications

Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

Convergence and stability estimates in difference setting for time‐fractional parabolic equations with functional delay

On the Novel Finite-Time Stability Results for Uncertain Fractional Delay Differential Equations Involving Noninstantaneous Impulses

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