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Anguraj, A.,Vinodkumar, A. The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.3
This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.
A. Anguraj,A.Vinodkumar 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation
Karthikeyan, K.,Anguraj, A. The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.1
In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.
K. Karthikeyan,A. Anguraj 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.1
In this paper, we prove the existence of mild solutions for a first order impulsive neutral diffrerential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation . By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established .
Existence Results for First Order Impulsive Functional Differential Equations in Banach Spaces
M. Mallika Arjunan,A. Anguraj 한국산업응용수학회 2007 Journal of the Korean Society for Industrial and A Vol.11 No.1
In this paper we prove the existence mild solutions of a first order impulsive initial value problems for functional differential equations in Banach spaces. The results are obtained by using the Lerey-Schauder nonlinear alternative fixed theorem.
CHALISHAJAR, DIMPLEKUMAR,RAMKUMAR, K.,ANGURAJ, A. The Korean Society for Computational and Applied M 2022 Journal of applied and pure mathematics Vol.4 No.1/2
The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.
Dimplekumar Chalishajar,K. Ramkumar,A. Anguraj 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.1
The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter \mathtt{H}\in (\frac{1}{2}, 1). We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.
K. RAMKUMAR,K. RAVIKUMAR,DIMPLEKUMAR CHALISHAJAR,A. ANGURAJ,MAMADOU ABDOUL DIOP The Korean Society for Computational and Applied M 2023 Journal of applied and pure mathematics Vol.5 No.1/2
This paper is concerned by the controllability results of impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, Krasnoselkii fixed point method and the theory of resolvent operator in the sense of Grimmer. A practical example is provided to illustrate the viability of the abstract result of this work.
K. Ramkumar,K. Ravikumar,Dimplekumar Chalishajar,A. Anguraj,Mamadou Abdoul Diop 한국전산응용수학회 2023 Journal of Applied and Pure Mathematics Vol.5 No.1
This paper is concerned by the controllability results of impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, Krasnoselkii fixed point method and the theory of resolvent operator in the sense of Grimmer. A practical example is provided to illustrate the viability of the abstract result of this work.
Dimplekumar Chalishajar,A. Anguraj,K. Ravikumar,K. Malar 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.5
This manuscript deals with the exact (complete) controllability of semilinear stochastic differential equations with infinite delay and Poisson jumps utilizing some basic and readily verified conditions. The results are obtained by using fixed-point approach and by using advance phase space definition for infinite delay part. We have used the axiomatic definition of the phase space in terms of stochastic process to consider the time delay of the system. An infinite delay along with the Poisson jump is the new investigation for the given stochastic system. An example is given to illustrate the effectiveness of the results.