On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps

Krishnan Thiagu

doi:doi:10.11648/j.ajam.20210902.13

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On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps

Krishnan Thiagu

Published in American Journal of Applied Mathematics (Volume 9, Issue 2)

Received: 4 February 2021 Accepted: 27 March 2021 Published: 26 April 2021

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Abstract

The main scope of this paper is to focus the approximate controllability of second order (q∈(1,2]) fractional impulsive stochastic differential system with nonlocal, state-dependent delay and Poisson umps in Hilbert spaces. The existence of mild solutions is derived by using Schauder fixed point theorem. Sufficient conditions for the approximate controllability are established by under the assumptions that the corresponding linear system is approximately controllable and it is checked by using Lebesgue dominated convergence theorem. The main results are completly based on the results that the existence and approximate controllability of the fractional stochastic system of order 1C_a(t)}_t≥0, new set of novel sufficient conditions and methods adopted directly from deterministic fractional equations for the second order nonlinear impulsive fractional nonlocal stochastic differential systems with state-dependent delay and Poisson jumps in Hildert space H. Finally an example is added to illustrate the main results.

Published in	American Journal of Applied Mathematics (Volume 9, Issue 2)
DOI	10.11648/j.ajam.20210902.13
Page(s)	52-63
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Approximate Controllability, Fixed-Point Theorem, Fractional Stochastic Differential System, Hilbert Space, Poisson Jumps

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APA Style

Krishnan Thiagu. (2021). On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps. American Journal of Applied Mathematics, 9(2), 52-63. https://doi.org/10.11648/j.ajam.20210902.13

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ACS Style

Krishnan Thiagu. On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps. Am. J. Appl. Math. 2021, 9(2), 52-63. doi: 10.11648/j.ajam.20210902.13

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AMA Style

Krishnan Thiagu. On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps. Am J Appl Math. 2021;9(2):52-63. doi: 10.11648/j.ajam.20210902.13

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@article{10.11648/j.ajam.20210902.13,
  author = {Krishnan Thiagu},
  title = {On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps},
  journal = {American Journal of Applied Mathematics},
  volume = {9},
  number = {2},
  pages = {52-63},
  doi = {10.11648/j.ajam.20210902.13},
  url = {https://doi.org/10.11648/j.ajam.20210902.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210902.13},
  abstract = {The main scope of this paper is to focus the approximate controllability of second order (q∈(1,2]) fractional impulsive stochastic differential system with nonlocal, state-dependent delay and Poisson umps in Hilbert spaces. The existence of mild solutions is derived by using Schauder fixed point theorem. Sufficient conditions for the approximate controllability are established by under the assumptions that the corresponding linear system is approximately controllable and it is checked by using Lebesgue dominated convergence theorem. The main results are completly based on the results that the existence and approximate controllability of the fractional stochastic system of order 1Ca(t)}t≥0, new set of novel sufficient conditions and methods adopted directly from deterministic fractional equations for the second order nonlinear impulsive fractional nonlocal stochastic differential systems with state-dependent delay and Poisson jumps in Hildert space H. Finally an example is added to illustrate the main results.},
 year = {2021}
}

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TY  - JOUR
T1  - On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps
AU  - Krishnan Thiagu
Y1  - 2021/04/26
PY  - 2021
N1  - https://doi.org/10.11648/j.ajam.20210902.13
DO  - 10.11648/j.ajam.20210902.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 52
EP  - 63
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20210902.13
AB  - The main scope of this paper is to focus the approximate controllability of second order (q∈(1,2]) fractional impulsive stochastic differential system with nonlocal, state-dependent delay and Poisson umps in Hilbert spaces. The existence of mild solutions is derived by using Schauder fixed point theorem. Sufficient conditions for the approximate controllability are established by under the assumptions that the corresponding linear system is approximately controllable and it is checked by using Lebesgue dominated convergence theorem. The main results are completly based on the results that the existence and approximate controllability of the fractional stochastic system of order 1Ca(t)}t≥0, new set of novel sufficient conditions and methods adopted directly from deterministic fractional equations for the second order nonlinear impulsive fractional nonlocal stochastic differential systems with state-dependent delay and Poisson jumps in Hildert space H. Finally an example is added to illustrate the main results.
VL  - 9
IS  - 2
ER  -

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Author Information

Krishnan Thiagu

Department of Mathematics, Kandaswami Kandar’s College, Velur (Namakkal), Tamilnadu, India

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APA Style

Krishnan Thiagu. (2021). On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps. American Journal of Applied Mathematics, 9(2), 52-63. https://doi.org/10.11648/j.ajam.20210902.13

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ACS Style

Krishnan Thiagu. On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps. Am. J. Appl. Math. 2021, 9(2), 52-63. doi: 10.11648/j.ajam.20210902.13

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AMA Style

Krishnan Thiagu. On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps. Am J Appl Math. 2021;9(2):52-63. doi: 10.11648/j.ajam.20210902.13

Copy | Download

@article{10.11648/j.ajam.20210902.13,
  author = {Krishnan Thiagu},
  title = {On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps},
  journal = {American Journal of Applied Mathematics},
  volume = {9},
  number = {2},
  pages = {52-63},
  doi = {10.11648/j.ajam.20210902.13},
  url = {https://doi.org/10.11648/j.ajam.20210902.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210902.13},
  abstract = {The main scope of this paper is to focus the approximate controllability of second order (q∈(1,2]) fractional impulsive stochastic differential system with nonlocal, state-dependent delay and Poisson umps in Hilbert spaces. The existence of mild solutions is derived by using Schauder fixed point theorem. Sufficient conditions for the approximate controllability are established by under the assumptions that the corresponding linear system is approximately controllable and it is checked by using Lebesgue dominated convergence theorem. The main results are completly based on the results that the existence and approximate controllability of the fractional stochastic system of order 1Ca(t)}t≥0, new set of novel sufficient conditions and methods adopted directly from deterministic fractional equations for the second order nonlinear impulsive fractional nonlocal stochastic differential systems with state-dependent delay and Poisson jumps in Hildert space H. Finally an example is added to illustrate the main results.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps
AU  - Krishnan Thiagu
Y1  - 2021/04/26
PY  - 2021
N1  - https://doi.org/10.11648/j.ajam.20210902.13
DO  - 10.11648/j.ajam.20210902.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 52
EP  - 63
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20210902.13
AB  - The main scope of this paper is to focus the approximate controllability of second order (q∈(1,2]) fractional impulsive stochastic differential system with nonlocal, state-dependent delay and Poisson umps in Hilbert spaces. The existence of mild solutions is derived by using Schauder fixed point theorem. Sufficient conditions for the approximate controllability are established by under the assumptions that the corresponding linear system is approximately controllable and it is checked by using Lebesgue dominated convergence theorem. The main results are completly based on the results that the existence and approximate controllability of the fractional stochastic system of order 1Ca(t)}t≥0, new set of novel sufficient conditions and methods adopted directly from deterministic fractional equations for the second order nonlinear impulsive fractional nonlocal stochastic differential systems with state-dependent delay and Poisson jumps in Hildert space H. Finally an example is added to illustrate the main results.
VL  - 9
IS  - 2
ER  -

Copy | Download