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Existence and controllability results for Sobolev-type fractional impulsive stochastic differential equations with infinite delay

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Języki publikacji
EN
Abstrakty
EN
In this paper, we prove the existence of mild solutions for Sobolev-type fractional impulsive stochastic di erential equations with in nite delay in Hilbert spaces. In addition, the controllability of the system with nonlocal conditions and in nite delay is studied. An example is provided to illustrate the obtained theory.
Rocznik
Tom
Strony
37--58
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
  • Department of Mathematics and Computer Sciences, University of Adrar, Algeria
autor
  • Department of Mathematics and Computer Sciences, University of Adrar, Algeria
Bibliografia
  • [1] H.M. Ahmed, Sobolev-Type Fractional Stochastic Integrodifferential Equations with Nonlocal Conditions in Hilbert Space, J. Theor. Probab. 30 (2017) 771-783.
  • [2] J. Bao, Z. Hou and C. Yuan, Stability in distribution of mild solutions to stochastic partial differential equations, Pro. American Math. Soc. 138 6 (2010) 2169-2180.
  • [3] J.H. Bao, Z.T. Hou, Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients, Comput. Math. Appl. 59 (2010) 207-214.
  • [4] A. Benchaabane, R. Sakthivel, Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficients, Journal of Computational and Applied Mathematics 312 (2017) 65-73.
  • [5] A. Boudaoui, A. Slama, Approximate controllability of nonlinear fractional impulsive stochastic differential equations with nonlocal conditions and infinite delay, Nonlinear Dynamics and Systems Theory 16 1 (2016) 35-48.
  • [6] J. Cao, Q. Yang, Z. Huang and Q. Liu, Asymptotically almost periodic solutions of stochastic functional differential equations, Appl. Math. Comput. 218 (2011) 1499-1511.
  • [7] J. Cao, Q. Yang and Z. Huang, On almost periodic mild solutions for stochastic functional differential equations, Nonlinear Anal. RWA 13 (2012) 275-286.
  • [8] M. Caputo, Elasticitae Dissipazione, Zanichelli, Bologna, 1969.
  • [9] Y.K. Chang, Z.H. Zhao, G.M. N'Guerekata and R. Ma, Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations, Nonlinear Anal. RWA 12 (2011) 1130-1139.
  • [10] J. Dabas, A. Chauhan and M. Kumar, Existence of the mild solutions for impulsive fractional equations with infinite delay, Int. J. Differ. Equ., Volume 2011 (2011) Article ID 793023, 20 pages.
  • [11] A. Debbouche, J.J. Nieto, Sobolev type fractional abstract evolution equations with nonlocal conditions and optimal multi-controls, Applied Mathematics and Computation 245 (2014) 74-85.
  • [12] A. Debbouche, D.F.M. Torres, Sobolev type fractional dynamic equations and optimal multi-integral controls with fractional nonlocal conditions, Fractional Calculus and Applied Analysis 18 (2015) 95-121.
  • [13] M. Feckan, J. Wang and Y. Zhou, Controllability of fractional functional evolution equations of Sobolev type via characteristic solution operators, Journal of Optimization Theory and Applications 156 (2013) 79-95.
  • [14] I. Karatzas, S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, Berlin 1991.
  • [15] M. Kerboua, A. Debbouche and D. Baleanu, Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces, Electronic Journal of Qualitative Theory of Differential Eqations 58 (2014) 1-16.
  • [16] M.A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, New York 1964.
  • [17] E. Lakhel, M.A. McKibben, Controllability of neutral stochastic integro-differential evolution equations driven by a fractional Brownian motion. Afr. Mat. 7 (2010) 1-14.
  • [18] F. Li, J. Liang and H.K. Xu, Existence of mild solutions for fractional integro-differential equations of Sobolev type with nonlocal conditions, Journal of Mathematical Analysis and Applications 391 (2012) 510-525.
  • [19] K. Li, J. Peng, Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014) 941-959.
  • [20] N.I. Mahmudov, Existence and approximate controllability of Sobolev type fractional stochastic evolution equations, Bulletin of the Polish Academy of Sciences Technical Sciences 62 2 (2014) 205-215.
  • [21] X. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, UK 1997.
  • [22] P. Revathi, R. Sakthivel and Y. Ren, Stochastic functional differential equations of Sobolev-type with infinite delay, Statistics and Probability Letters 109 (2016) 68-77.
  • [23] Y. Ren, D.D. Sun, Second-order neutral stochastic evolution equations with infinite delay under Caratheodory conditions, J. Optim. Theory Appl. 147 3 (2010) 569-582.
  • [24] Y. Ren, Q. Zhou and L. Chen, Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay, J. Optim. Theory Appl. 149 (2011) 315-331.
  • [25] R. Sakthivel, P. Revathi and Y. Ren, Existence of solutions for nonlinear fractional stochastic differential equations, Nonlinear Analysis 81 (2013) 70-86.
  • [26] X.B. Shu, Y. Lai and Y. Chen, The existence of mild solutions for impulsive fractional partial differential equations, Nonlinear Anal. TMA 75 5 (2011) 2003-2011.
  • [27] A. Slama, A. Boudaoui, Approximate controllability of fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay, Annals of Differential Equation 2 (2015) 127-139.
  • [28] F. Wei, K. Wang, The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay, J. Math. Anal. Appl. 331 (2007) 516-531.
  • [29] Z. Yan, F. Lu, Existence results for a new class of fractional impulsive partial neutral stochastic integro-differential equations with infinte delay, Journal of Applied Analysis and Computation 5 3 August (2015) 329-346.
  • [30] Y. Zhou, F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl. 59 (2010) 1063-1077.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-d3ac79e6-964e-4940-87e9-d160bfe76066
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