Research article

Well posedness of second-order impulsive fractional neutral stochastic differential equations

  • Received: 04 March 2021 Accepted: 24 May 2021 Published: 21 June 2021
  • MSC : 34K30, 60H60

  • In this manuscript, we investigate a class of second-order impulsive fractional neutral stochastic differential equations (IFNSDEs) driven by Poisson jumps in Banach space. Firstly, sufficient conditions of the existence and the uniqueness of the mild solution for this type of equations are driven by means of the successive approximation and the Bihari's inequality. Next we get the stability in mean square of the mild solution via continuous dependence on initial value.

    Citation: Ramkumar Kasinathan, Ravikumar Kasinathan, Dumitru Baleanu, Anguraj Annamalai. Well posedness of second-order impulsive fractional neutral stochastic differential equations[J]. AIMS Mathematics, 2021, 6(9): 9222-9235. doi: 10.3934/math.2021536

    Related Papers:

  • In this manuscript, we investigate a class of second-order impulsive fractional neutral stochastic differential equations (IFNSDEs) driven by Poisson jumps in Banach space. Firstly, sufficient conditions of the existence and the uniqueness of the mild solution for this type of equations are driven by means of the successive approximation and the Bihari's inequality. Next we get the stability in mean square of the mild solution via continuous dependence on initial value.



    加载中


    [1] A. Anguraj, K. Ramkumar, E. M. Elsayed, Existence, uniqueness and stability of impulsive stochastic partial neutral functional differential equations with infinite delays driven by a fractional Brownian motion, Discontinuity, Nonlinearity, and Complexity, 9 (2020), 327–337. doi: 10.5890/DNC.2020.06.012
    [2] A. Anguraj, K. Ravikumar, Existence and stability results of impulsive stochastic partial neutral functional differential equations with infinite delays and Poisson jumps, Journal of Applied Nonlinear Dynamics, 9 (2020), 245–255.
    [3] A. Anguraj, K. Ravikumar, Existence and stability results for impulsive stochastic functional integrodifferential equations with Poisson jumps, Journal of Applied Nonlinear Dynamics, 8 (2019), 407–417. doi: 10.5890/JAND.2019.09.005
    [4] P. Balasubramaniam, S. Saravanakumar, K. Ratnavelu, Study a class of Hilfer fractional stochastic integrodifferential equations with Poisson jumps, Stoch. Anal. Appl.,, 36 (2018), 1021–1036.
    [5] A. Chadha, D. N. Pandey, Existence results for an impulsive neutral stochastic fractional integrodifferential equation with infinite delay, Nonlinear Analysis, 128 (2015), 149–175. doi: 10.1016/j.na.2015.07.018
    [6] K. Dhanalakshmi, P. Balasubramaniam, Stability result of higher-order fractional neutral stochastic differential system with infinite delay driven by Poisson jumps and Rosenblatt process, Stoch. Anal. Appl., 38 (2019), 352–372.
    [7] E. Hausenblas, SPDEs driven by Poisson random measure with non Lipschitz coefficients:existence results, Probab. Theory Rel., 137 (2006), 161–200. doi: 10.1007/s00440-006-0501-8
    [8] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam: Elsevier Science, Vol 204, 2006.
    [9] J. Luo, T. Taniguchi, The existence and uniqueness for non-Lipschitz stochastic neutral delay evolution equations driven by Poisson jumps, Stoch. Dyn., 9 (2009), 135–152. doi: 10.1142/S0219493709002592
    [10] X. Mao, Stochastic Differential Equations and Applications, Chichester: Horwood, 1997.
    [11] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, New York: John Wiley, 1993.
    [12] M. A. Ouahra, B. Boufoussi, E. Lakhel, Existence and stability for stochastic impulsive neutral partial differential equations driven by Rosenblatt process with delay and Poisson jumps, Commun. Stoch. Anal., 11 (2017), 99–117.
    [13] I. Podlubny, Fractional Differential Equations, London: Academic Press, 1999.
    [14] G. D. Prato, J. Zabczyk, Stochastic Equations in Infinite Dimensions, London: Cambridge University Press, 2014.
    [15] Y. Ren, R. Sakthivel, Existence, uniqueness and stability of mild solutions for second-order neutral stochastic evolution equations with infinite delay and Poisson jumps, J. Math. Phys., 53 (2012), 073517. doi: 10.1063/1.4739406
    [16] F. A. Rihan, C. Rajivganthi, P. Muthukumar, Fractional stochastic differential equations with Hilfer fractional derivative: Poisson jumps and optimal control, Disc. Dyn. Nat. Soc., 2017 (2017).
    [17] P. Tamilalagan, P. Balasubramaniam, Existence results for semilinear fractional stochastic evolution inclusions driven by Poisson jumps, In Mathematical Analysis and Its Applications, Springer, (2014), 477–487.
    [18] S. Xie, Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay, Fract. Calc. Appl. Anal., 17 (2014), 1158–1174.
    [19] S. Zhao, M. Song, Stochastic impulsive fractional differential evolution equations with infinite delay, Filomat, 31 (2017), 4261–4274. doi: 10.2298/FIL1713261Z
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2068) PDF downloads(121) Cited by(1)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog