Existence and Uniqueness Result for a Class of Impulsive Delay Differential Equations

Ugboh, J. A.; Esuabana, I. M.

doi:10.22161/ijcmp.2.4.1

Cited by 2 publications

(1 citation statement)

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“…In this study, a system of first-order impulsive differential equations with continuous time-dependent delays and fixed moments of impulse is formulated. Some recent results in impulsive delay differential equations with constant impulsive jumps can be seen in [7][8][9][10][11][12][13][14].…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

Formulation of Impulsive Differential Equations with Time-Dependent Continuous Delay

Esuabana¹

2018

AJAM

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Research in impulsive delay differential equations has been undergoing some exciting growth in recent times. This to a large extent can be attributed to the quest by mathematicians in particular and the science community as a whole to unveil nature the way it truly is. The realization that differential equations, in general, and indeed impulsive delay differential equations are very important models for describing the true state of several real-life processes/phenomena may have been the tunic. One can attest that in most human processes or natural phenomena, the present state is most often affected significantly by their past state and those that were thought of as continuous may indeed undergo abrupt change at several points or even be stochastic. In this study, a special strictly ascending continuous delay is constructed for a class of system of impulsive differential equations. It is demonstrated that even though the dynamics of the system and the delay have ideal continuity properties, the right side may not even have limits at some points due to the impact of past impulses in the present. The integral equivalence of the formulated system of equations is also obtained via a scheme similar to that of Perron by making use of certain assumptions.

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Section: Introduction and Statement Of Problemmentioning

confidence: 99%

Formulation of Impulsive Differential Equations with Time-Dependent Continuous Delay

Esuabana¹

2018

AJAM

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On the Novel Auxiliary Lyapunov Function and Uniform Asymptotic Practical Stability of Nonlinear Impulsive Caputo Fractional Differential Equations via New Modelled Generalized Dini Derivative

J. E.,

O. O.,

J. U.

et al. 2024

African Journal of Mathematics and Statistics Studies

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In this paper, the uniform asymptotic practical stability of nonlinear impulsive Caputo fractional differential equations with fixed moments of impulse is examined using an auxiliary Lyapunov functions which are analogues of vector Lyapunov functions. Together with comparison results, sufficient conditions for the uniform practical stability as well as the uniform asymptotic practical stability of the impulsive Caputo fractional order systems are established. An illustrative example is given to confirm the suitability of the obtained results.

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Existence and Uniqueness Result for a Class of Impulsive Delay Differential Equations

Cited by 2 publications

References 0 publications

Formulation of Impulsive Differential Equations with Time-Dependent Continuous Delay

Formulation of Impulsive Differential Equations with Time-Dependent Continuous Delay

On the Novel Auxiliary Lyapunov Function and Uniform Asymptotic Practical Stability of Nonlinear Impulsive Caputo Fractional Differential Equations via New Modelled Generalized Dini Derivative

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