Some generalized Gronwall-Bellman-Bihari type integral inequalities with application to fractional stochastic differential equation

Hussain, Sabir; Sadia, Halima; Aslam, Sidra

doi:10.2298/fil1903815h

Cited by 5 publications

(2 citation statements)

References 7 publications

(9 reference statements)

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“…Remark On the basis of the fractional‐order inequality [61], quasi‐uniform stability criterion of FONNDDDs was obtained in Naifar et al [54]. The corresponding criterion is an inequality which is related to the Mittag‐Leffler function.…”

Section: Resultsmentioning

confidence: 99%

Improved quasi‐uniform stability criterion of fractional‐order neural networks with discrete and distributed delays

2022

Asian Journal of Control

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This article mainly investigates the quasi‐uniform stability of fractional‐order neural networks with time discrete and distributed delays (FONNDDDs). First, a novel fractional‐order Gronwall inequality with discrete and distributed delays (FOGIDDDs) is established; it can be used to study the stability of a variety of fractional‐order systems with discrete and distributed delays (FOSDDDs). Second, on the basis of this inequality and Leray‐Schauder alternative theorem, the existence and uniqueness results for the FONNDDDs are proved. Third, an improved criterion for the quasi‐uniform stability of FONNDDDs is obtained in terms of this inequality. Ultimately, one numerical example is provided to expound the effectiveness and the superiority of the proposed result.

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Section: Resultsmentioning

confidence: 99%

Improved quasi‐uniform stability criterion of fractional‐order neural networks with discrete and distributed delays

2022

Asian Journal of Control

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“…Lemma 1 (see [24]). Let a(t), b(t), g(t), and u(t) be nonnegative functions on I � [0, T), T ≤ + ∞, α ∈ (0, 1).…”

Section: Definitionmentioning

confidence: 99%

Improved Quasiuniform Stability for Fractional Order Neural Nets with Mixed Delay

Naifar

Jmal

Nagy

et al. 2020

Mathematical Problems in Engineering

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In the present paper, a quasiuniform stability result for fractional order neural networks with mixed delay is developed, based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are derived to ensure the quasiuniform stability of the considered neural nets system. A clarification example is carried out not only to validate the authors’ theoretical results but also to show the superiority of the developed work (in terms of improved stability), compared with other similar works already published in the literature.

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Some New Gronwall-Type Integral Inequalities and their Applications to Finite-Time Stability of Fractional-Order Neural Networks with Hybrid Delays

Yang

Zhang

et al. 2023

Neural Process Lett

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Some generalized Gronwall-Bellman-Bihari type integral inequalities with application to fractional stochastic differential equation

Cited by 5 publications

References 7 publications

Improved quasi‐uniform stability criterion of fractional‐order neural networks with discrete and distributed delays

Improved quasi‐uniform stability criterion of fractional‐order neural networks with discrete and distributed delays

Improved Quasiuniform Stability for Fractional Order Neural Nets with Mixed Delay

Some New Gronwall-Type Integral Inequalities and their Applications to Finite-Time Stability of Fractional-Order Neural Networks with Hybrid Delays

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