Qualification: 
Ph.D, MPhil, MSc, BSc
a_vinodkumar@cb.amrita.edu

Dr. Vinodkumar A. currently serves as Assistant Professor (Sr. G)  at the department of Mathematics, School of Engineering, Coimbatore Campus.

Publications

Publication Type: Journal Article

Year of Publication Publication Type Title

2017

Journal Article

Dr. Vinodkumar A., “Some results in stochastic functional integro-differential equations with infinite delays”, International Journal of Dynamical Systems and Differential Equations, vol. 7, pp. 36-50, 2017.[Abstract]


In this paper, we study the results on averaging principle and stability of mild solutions for stochastic functional integro-differential equation with non-Lipschitz condition. We establish the result by the method of successive approximation and Bihari's inequality under the theory of resolvent operators. Finally, an example is provided for demonstration. Copyright © 2017 Inderscience Enterprises Ltd.

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2016

Journal Article

Dr. Vinodkumar A., Malar, K., GOWRISANKAR, M., and MOHANKUMAR, P., “Existence, Uniqueness and Stability of Random Impulsive Fractional Differential Equations”, Acta Mathematica Scientia, vol. 36, pp. 428 - 442, 2016.[Abstract]


In this article, we study the existence, uniqueness, stability through continuous dependence on initial conditions and Hyers-Ulam-Rassias stability results for random impulsive fractional differential systems by relaxing the linear growth conditions. Finally, we give examples to illustrate its applications.

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2016

Journal Article

Dr. Vinodkumar A. and Rakkiyappan, R., “Exponential Stability Results for Fixed and Random Type Impulsive Hopfield Neural Networks”, International Journal of Computing Science and Mathematics, vol. 7, pp. 1–19, 2016.[Abstract]


This article presents the exponential stability results on impulsive Hopfield neural networks (IHNNs) via variation of parameters and fixed point theory. The study is mainly considering two types of IHNNs, namely fixed and random type IHNNs. A numerical example is also presented to validate the theoretical results. More »»

2016

Journal Article

S. Vijay, Loganathan, C., and Dr. Vinodkumar A., “Approximate controllability of random impulsive semilinear control systems”, Nonlinear Studies, vol. 23, pp. 273-280, 2016.[Abstract]


In this paper, we study the existence of approximate controllability of random impulsive semilinear control system under a sufficient condition with non-densely defined system. Finally, examples are given to illustrate the applications of the abstract results. More »»

2016

Journal Article

Dr. Vinodkumar A., GOWRISANKAR, M. U. T. H. U. S. A. M. Y., and MOHANKUMAR, P. R. A. T. H. I. B. A. N., “Existence and Stability Results on Nonlinear Delay Integro-Differential Equations with Random Impulses.”, Kyungpook Mathematical Journal, vol. 56, pp. 431 - 450, 2016.[Abstract]


In this paper, the existence, uniqueness, stability via continuous dependence and Ulam stabilities of nonlinear integro-differential equations with random impulses are studied under sufficient condition. The results are obtained by using Leray-Schauder alternative fixed point theorem and Banach contraction principle. More »»

2016

Journal Article

S. Vijay, Loganathan, C., and Dr. Vinodkumar A., “Approximate Controllability of Random Impulsive Semilinear Control Systems.”, Nonlinear Studies, vol. 23, pp. 273 - 280, 2016.[Abstract]


In this paper, we study the existence of approximate controllability of random impulsive semilinear control system under a sufficient condition with non-densely defined system. Finally, eximples are given to illustrate the applications of the abstract results. More »»

2016

Journal Article

C. Parthasarathy, M Arjunan, M., and Dr. Vinodkumar A., “Existence and Stability Solutions of Nonlinear Stochastic Functional Partial Integrodifferential Equations with Infinite Delay”, International Journal of Mathematics in Operational Research, vol. 9, pp. 65–78, 2016.[Abstract]


In this paper, we are focused upon the results on existence, uniqueness and stability of mild solution for stochastic functional integrodifferential equations with non-Lipschitz condition. The theory of resolvent operator is utilised to exhibit the existence of these mild solutions. The results are obtained by using the method of successive approximation and Bihari's inequality. Finally, an example is provided for demonstration.

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2015

Journal Article

Dr. Vinodkumar A., GOWRISANKAR, M., and MOHANKUMAR, P., “Existence, Uniqueness and stability of Random Impulsive Neutral Partial Differential Equations”, Journal of the Egyptian Mathematical Society, vol. 23, pp. 31 - 36, 2015.[Abstract]


Abstract In this paper, the existence, uniqueness and stability via continuous dependence of mild solution of neutral partial differential equations with random impulses are studied under sufficient condition via fixed point theory. More »»

2014

Journal Article

M. GOWRISANKAR, MOHANKUMAR, P., and Dr. Vinodkumar A., “Stability results of Random Impulsive Semilinear Differential Equations”, Acta Mathematica Scientia, vol. 34, pp. 1055 - 1071, 2014.[Abstract]


In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results. More »»

2014

Journal Article

Dr. Vinodkumar A., “Existence results for Random Impulsive Neutral Differential Inclusions with Lower Semicontinuous”, International Journal of Computing Science and Mathematics, vol. 5, pp. 151–164, 2014.[Abstract]


This article presents the results on existence of mild solutions for random impulsive neutral functional differential inclusions under sufficient conditions. The results are obtained by using the Krasnoselskii-Schaefer type fixed point theorem combined with the selection theorem of Berssan and Colombo for lower semicontinuous (LSC) maps with decomposable values. More »»

2013

Journal Article

R. Rakkiyappan, Pradeep, C., Dr. Vinodkumar A., and Rihan, F. A., “Dynamic Analysis for High-order Hopfield Neural Networks with Leakage Delay and Impulsive Effects”, Neural Computing and Applications, vol. 22, pp. 55–73, 2013.[Abstract]


This paper considers existence, uniqueness, and the global asymptotic stability for a class of High-order Hopfield neural networks with mixed delays and impulses. The mixed delays include constant delay in the leakage term (i.e., ``leakage delay'') and time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-dependent sufficient conditions are presented for the global asymptotic stability of the equilibrium point of the considered neural networks. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the applicability of the result. More »»

2013

Journal Article

A. Anguraj, Dr. Vinodkumar A., and Chang, Y. K., “EXISTENCE RESULTS ON IMPULSIVE STOCHASTIC FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH DELAYS”, 2013.

2013

Journal Article

C. .Parthasarathy, M. Arjunan, M., and Dr. Vinodkumar A., “Existence, Uniqueness and Stability of Neutral Stochastic Functional Integro-differential Evolution Equations with Infinite Delay”, International Journal of Computer Applications (0975 - 8887), vol. 65, pp. 1–7, 2013.[Abstract]


This article presents the results on existence, uniqueness and stability of mild solutions to neutral stochastic functional evolution integro-differential equations with non-Lipschitz condition and Lipschitz condition. The existence of mild solutions for the equations are discussed by means of semigroup theory and theory of resolvent operator. Under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari’s inequality. Moreover, an example is given to illustrate our results.

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2012

Journal Article

Dr. Vinodkumar A., “Existence Results on Random Impulsive Semilinear functional Differential Inclusions with Delays”, Ann. Funct. Anal, vol. 3, pp. 89–106, 2012.[Abstract]


This article presents the result on existence of mild solutions for random impulsive semilinear functional differential inclusions under sufficient conditions. The results are obtained by using the Martelli fixed point theorem and the fixed point theorem due to Covitz and Nadler.

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2012

Journal Article

Dr. Vinodkumar A., “Existence and Uniqueness of Solutions for Random Impulsive Differential Equation”, Malaya Journal of Matematik, vol. 1, pp. 8–13, 2012.[Abstract]


In this paper, we study the existence and uniqueness of the mild solutions for random impulsive differential equations through fixed point technique. An example is provided to illustrate the theory.

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2012

Journal Article

C. Pradeep, Dr. Vinodkumar A., and Rakkiyappan, R., “Delay-Dependent Exponential Stability Results for Uncertain Stochastic Hopfield Neural Networks with Interval Time-varying Delays”, Arabian Journal of Mathematics, vol. 1, pp. 227–239, 2012.[Abstract]


This paper is concerned with stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Both the cases of the time-varying delays which may be differentiable and may not be differentiable are considered in this paper. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay/interval-dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), by introducing some free-weighting matrices. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions. More »»

2011

Journal Article

A. Anguraj, Wu, S., and Dr. Vinodkumar A., “The existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness”, Nonlinear Analysis: Theory, Methods & Applications, vol. 74, pp. 331 - 342, 2011.[Abstract]


In this paper, the existence and exponential stability of mild solutions of semilinear differential equations with random impulses are studied under non-uniqueness in a real separable Hilbert space. The results are obtained by using the Leray–Schauder alternative fixed point theorem. More »»

2011

Journal Article

Dr. Vinodkumar A. and Anguraj, A., “Existence of random impulsive abstract neutral non-autonomous differential inclusions with delays”, Nonlinear Analysis: Hybrid Systems, vol. 5, pp. 413 - 426, 2011.[Abstract]


This article presents the results on existence of mild solutions of random impulsive neutral functional differential inclusions under sufficient conditions. The results are obtained by using the Dhage’s fixed point theorem. More »»

2011

Journal Article

Dr. Vinodkumar A. and Boucherif, A., “Existence Results for Stochastic Semilinear Differential Inclusions with nonlocal Conditions”, International Journal of Stochastic Analysis, vol. 2011, 2011.[Abstract]


We discuss existence results of mild solutions for stochastic differential inclusions subject to nonlocal conditions. We provide sufficient conditions in order to obtain a priori bounds on possible solutions of a one-parameter family of problems related to the original one. We, then, rely on fixed point theorems for multivalued operators to prove our main results.

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2010

Journal Article

A. Anguraj and Dr. Vinodkumar A., “EXISTENCE, UNIQUENESS AND STABILITY OF IMPULSIVE STOCHASTIC PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS”, Journal of Applied Mathematics and Informatics, vol. 28, pp. 739–751, 2010.

2009

Journal Article

A. Anguraj and Dr. Vinodkumar A., “Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays”, Electron. J. Qual. Theory Differ. Equ, vol. 2009, pp. 1–13, 2009.

2009

Journal Article

A. Anguraj and Dr. Vinodkumar A., “Existence and uniqueness of neutral functional differential equations with random impulses”, International Journal of Nonlinear Science, vol. 8, pp. 412–418, 2009.[Abstract]


In this paper, the existence and uniqueness of the solution of random impulsive neutral functional differential equation is investigated under sufficient condition. The results are obtained by using the Contraction principle.

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Publication Type: Conference Paper

Year of Publication Publication Type Title

2016

Conference Paper

A. L. P. Indhumathi and Dr. Vinodkumar A., “Existence and Uniqueness results for Random Impulsive Partial Differential equation over Real axis”, in International Journal of Applied Engineering Research (IJAER), 2016.

Faculty Research Interest: 
207
PROGRAMS
OFFERED
6
AMRITA
CAMPUSES
15
CONSTITUENT
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GRADE BY
NAAC, MHRD
8th
RANK(INDIA):
NIRF 2018
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INTERNATIONAL
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