Henry-Gronwall Integral Inequalities with “Maxima” and Their Applications to Fractional Differential Equations

Thiramanus, Phollakrit; Tariboon, Jessada; Ntouyas, Sotiris K.

doi:10.1155/2014/276316

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An Integral Inequality1

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Cited by 5 publications

(1 citation statement)

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“…On the other hand, from (26), since ∫ t 0 s α−1 Eα,α(−λs α )ds is nondecreasing with respect t, so does for…”

Section: An Integral Inequalitymentioning

confidence: 99%

Asymptotical stability of fractional order systems with time delay via an integral inequality

Zhou

Chen

et al. 2018

IET Control Theory & Applications

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In this paper, the asymptotical stability for several classes of fractional order differential systems with time delay is investigated. We firstly present an integral inequality by which the Halanay inequality is extended to fractional order case. Based on the generalized Halanay inequality, we establish several asymptotical stability conditions under which the fractional order systems with time delay are asymptotically stable. It is worth to note that these stability conditions are easy to check without resorting to the solution expression of the systems.

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“…On the other hand, from (26), since ∫ t 0 s α−1 Eα,α(−λs α )ds is nondecreasing with respect t, so does for…”

Section: An Integral Inequalitymentioning

confidence: 99%

Asymptotical stability of fractional order systems with time delay via an integral inequality

Zhou

Chen

et al. 2018

IET Control Theory & Applications

View full text Add to dashboard Cite

show abstract

Existence and finite-time stability results for impulsive fractional differential equations with maxima

Zhang

Wang

2015

J. Appl. Math. Comput.

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Some weakly singular Volterra integral inequalities with maxima in two variables

Sun

2023

J Inequal Appl

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Henry-Gronwall Integral Inequalities with “Maxima” and Their Applications to Fractional Differential Equations

Abstract: Some new weakly singular Henry-Gronwall type integral inequalities with “maxima” are established in this paper. Applications to Caputo fractional differential equations with “maxima” are also presented.

Cited by 5 publications

References 20 publications

Asymptotical stability of fractional order systems with time delay via an integral inequality

Asymptotical stability of fractional order systems with time delay via an integral inequality

Existence and finite-time stability results for impulsive fractional differential equations with maxima

Some weakly singular Volterra integral inequalities with maxima in two variables

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