Positive solutions of a nonlinear impulsive equation with periodic boundary conditions

Huseynov, Aydin

doi:10.1016/j.amc.2010.05.055

Cited by 8 publications

(3 citation statements)

References 11 publications

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“…e GDTM consisting of the generalized differential transformation (7) and its inverse transform (8) has increased the applications of the DTM to fractional differential equations. e basic simulations done by generalized differential transformation can be learned from [48], and the mostly applicable characteristics are specified by the following theorems.…”

Section: Generalized Differential Transform Schemementioning

confidence: 99%

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An Implementation of the Generalized Differential Transform Scheme for Simulating Impulsive Fractional Differential Equations

Odibat

Ertürk

Kumar³

et al. 2022

Mathematical Problems in Engineering

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In this research study, the generalized differential transform scheme has been applied to simulate impulsive differential equations with the noninteger order. One specific tool of the implemented scheme is that it converts the problems into a recurrence equation that finally leads easily to the solution of the considered problem. The validity and reliability of this method have successfully been accomplished by applying it to simulate the solution of some equations. It is shown that the considered method is very suitable and efficient for solving classes of fractional-order initial value problems for impulsive differential equations and might find wide applications.

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Section: Generalized Differential Transform Schemementioning

confidence: 99%

“…e theory and applications addressing such problems have been reported [1][2][3][4][5][6]. Recently, some interesting solutions' existence results for impulsive di erential equations have been explored largely; we suggest the reader to [7][8][9][10][11] and the papers therein.…”

Section: Introductionmentioning

confidence: 99%

An Implementation of the Generalized Differential Transform Scheme for Simulating Impulsive Fractional Differential Equations

Odibat

Ertürk

Kumar³

et al. 2022

Mathematical Problems in Engineering

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“…[38] dealt with the periodic solutions problem for impulsive differential equations. By using Lyapunov's second method and the contraction mapping principle, some conditions ensuring the existence and global attractiveness of unique periodic solutions were derived, and so on [37,84,101,26].…”

Section: Impulsive Delayed Systemsmentioning

confidence: 99%

Review of stability and stabilization for impulsive delayed systems

Xiao

Li²,

Xi³

et al. 2018

Mathematical Biosciences &Amp; Engineering

167

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This paper reviews some recent works on impulsive delayed systems (IDSs). The prime focus is the fundamental results and recent progress in theory and applications. After reviewing the relative literatures, this paper provides a comprehensive and intuitive overview of IDSs. Five aspects of IDSs are surveyed including basic theory, stability analysis, impulsive control, impulsive perturbation, and delayed impulses. Then the research prospect is given, which provides a reference for further study of IDSs theory.

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