Existence, uniqueness and stability of random impulsive neutral partial differential equations

Vinodkumar, A.; Gowrisankar, M.; Mohankumar, P.

doi:10.1016/j.joems.2014.01.005

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…When the impulses exist at random, this affects the nature of the differential system. For more work on the study of random impulsive differential equations, we refer the reader to [12][13][14][15][16][17][18] and the references therein. In particular, Anguraj et al [16] considered the existence and stability results for a class of random impulsive fractional pantograph equations, and Priyadharsini and Balasubramaniam [19] studied existence and uniqueness results for fuzzy fractional stochastic pantograph differential equations.…”

Section: Introductionmentioning

confidence: 99%

Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

Gao,

2024

Mathematics

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In this paper, we study the existence, uniqueness and Hyers–Ulam stability of a class of fractional stochastic pantograph equations with random impulses. Firstly, we establish sufficient conditions to ensure the existence of solutions for the considered equations by applying Schaefer’s fixed point theorem under relaxed linear growth conditions. Secondly, we prove the solution for the considered equations is Hyers–Ulam stable via Gronwall’s inequality. Moreover, the previous literature will be significantly generalized in our paper. Finally, an example is given to explain the efficiency of the obtained results.

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Section: Introductionmentioning

confidence: 99%

Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

Gao,

2024

Mathematics

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“…Moreover, Anguraj and Vinodkumar [16] investigated the existence and uniqueness of neutral functional dierential equations with random impulses. Vinodkumar et al [17] established the existence and stability results on random impulsive neutral partial dierential equations. Recently, Li Zihan et al [18] studied the existence of solutions for SturmLiouville dierential equation with random impulses and boundary value problems using Green functions and Dhage's xed point theorem.…”

Section: Introductionmentioning

confidence: 99%

Existence Uniqueness and Stability of Nonlocal Neutral Stochastic Differential Equations with Random Impulses and Poisson Jumps

Chalishajar

KUMARK²,

RAVİKUMAR³

et al. 2022

Results in Nonlinear Analysis

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This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsiveneutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove theexistence of mild solutions to this equation using the Banach fixed point theorem. Next, we prove thestability via continuous dependence initial value. Our study extends the work of Wang and Wu [15] wherethe time delay is addressed by the prescribed phase space B (defined in Section 3). An example is given toillustrate the theory.

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“…To the best of our knowledge, in the setting of impulsive RDEs, the contributions are still scarce and they have mainly focused on theoretical questions about existence and uniqueness of solutions. For example, in [35] one studies existence, uniqueness and stability via continuous dependence of weak solutions of neutral partial differential equations using the fixed point theory. In [37], sufficient conditions for p-moment boundedness of nonlinear impulsive RDEs are presented.…”

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confidence: 99%

Probabilistic analysis of a class of impulsive linear random differential equations forced by stochastic processes admitting Karhunen-Loève expansions

López

Delgadillo-Aleman

Kú-Carrillo

et al. 2022

DCDS-S

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<p style='text-indent:20px;'>We study a full randomization of the complete linear differential equation subject to an infinite train of Dirac's delta functions applied at different time instants. The initial condition and coefficients of the differential equation are assumed to be absolutely continuous random variables, while the external or forcing term is a stochastic process. We first approximate the forcing term using the Karhunen-Loève expansion, and then we take advantage of the Random Variable Transformation method to construct a formal approximation of the first probability density function (1-p.d.f.) of the solution. By imposing mild conditions on the model parameters, we prove the convergence of the aforementioned approximation to the exact 1-p.d.f. of the solution. All the theoretical findings are illustrated by means of two examples, where different types of probability distributions are assumed to model parameters.</p>

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Existence, uniqueness and stability of random impulsive neutral partial differential equations

Cited by 8 publications

References 13 publications

Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

Existence Uniqueness and Stability of Nonlocal Neutral Stochastic Differential Equations with Random Impulses and Poisson Jumps

Probabilistic analysis of a class of impulsive linear random differential equations forced by stochastic processes admitting Karhunen-Loève expansions

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