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Chalishajar, Dimplekumar N.,Acharya, Falguni S. Korean Mathematical Society 2011 대한수학회보 Vol.48 No.4
In this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. The controllability results in infinite dimensional space has been proved without compactness on the family of Cosine operators.
CHALISHAJAR, DIMPLEKUMAR N.,RAMESH, R. The Korean Society for Computational and Applied M 2022 Journal of applied and pure mathematics Vol.4 No.1/2
This work considers the existence and uniqueness of fuzzy solutions for impulsive abstract partial neutral functional differential systems. To establish the existence and uniqueness, we apply the concept of impulse, semi group theory and suitable fixed point theorem.
CHALISHAJAR, DIMPLEKUMAR,RAMKUMAR, K.,RAVIKUMAR, K.,COX, EOFF The Korean Society for Computational and Applied M 2022 Journal of applied and pure mathematics Vol.4 No.3/4
This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.
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,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.
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.
Dimplekumar Chalishajar,K. Ramkumar,K. Ravikumar 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.5
This manuscript addressed, the existence and uniqueness result for random impulsive stochastic functional differential equations with finite time delays. The study of random impulsive stochastic system is a new area of research. We interpret the meaning of a stochastic derivative and how it differs from the classical derivative. We prove the existence and uniqueness of mild solutions to the equations by using the successive approximation method. We conclude the article with some interesting future extension. This work extends the work of [18,12,20]. Finally, an example is given to illustrate the theoretical result.
Existence results for coupled hybrid Hadamard fractional differential equations in Banach spaces
Dimplekumar Chalishajar,P. Karthikeyan,K. Buvaneswari 한국전산응용수학회 2021 Journal of Applied and Pure Mathematics Vol.3 No.5
The purpose of this paper is to find the existence results for a coupled system of nonlinear hybrid Hadamard fractional differential equations associated with the initial conditions. The obtained result is a new configuration in the coupled system and it is studied using the classical fixed point theorem due to Dhage. The nonlinearities in the coupled system of equations depend on the unknown functions as well as their lower order fractional derivatives. Sufficient criteria ensuring the existence of solutions for the given problem are presented. Our results are new in the given configuration and are well illustrated with the aid of example.
DIMPLEKUMAR, CHALISHAJAR,K., RAMKUMAR,K., RAVIKUMAR The Korean Society for Computational and Applied M 2022 Journal of applied and pure mathematics Vol.4 No.5
This manuscript addressed, the existence and uniqueness result for random impulsive stochastic functional differential equations with finite time delays. The study of random impulsive stochastic system is a new area of research. We interpret the meaning of a stochastic derivative and how it differs from the classical derivative. We prove the existence and uniqueness of mild solutions to the equations by using the successive approximation method. We conclude the article with some interesting future extension. This work extends the work of [18, 12, 20]. Finally, an example is given to illustrate the theoretical result.
D.N., CHALISHAJAR,A., ANGURAJ,K., RAVIKUMAR,K., MALAR The Korean Society for Computational and Applied M 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.