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Tunc, Cemil, Oktan, Zozan. (1403). Improved new qualitative results on stochastic delay differential equations of second order. سامانه مدیریت نشریات علمی, 12(1), 67-76. doi: 10.22034/cmde.2022.52821.2229
Cemil Tunc; Zozan Oktan. "Improved new qualitative results on stochastic delay differential equations of second order". سامانه مدیریت نشریات علمی, 12, 1, 1403, 67-76. doi: 10.22034/cmde.2022.52821.2229
Tunc, Cemil, Oktan, Zozan. (1403). 'Improved new qualitative results on stochastic delay differential equations of second order', سامانه مدیریت نشریات علمی, 12(1), pp. 67-76. doi: 10.22034/cmde.2022.52821.2229
Tunc, Cemil, Oktan, Zozan. Improved new qualitative results on stochastic delay differential equations of second order. سامانه مدیریت نشریات علمی, 1403; 12(1): 67-76. doi: 10.22034/cmde.2022.52821.2229

Improved new qualitative results on stochastic delay differential equations of second order

Computational Methods for Differential Equations
مقاله 6، دوره 12، شماره 1، فروردین 2024، صفحه 67-76    اصل مقاله (294.6 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.52821.2229
نویسندگان
Cemil Tunc* ؛ Zozan Oktan
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey.
چکیده
This paper deals with a class of stochastic delay differential equations (SDDEs) of second order with multiple delays. Here, two main and novel results are proved on stochastic asymptotic stability and stochastic boundedness of solutions of the considered SDDEs. In the proofs of results, the Lyapunov-Krasovskii functional (LKF) method is used as the main tool. A comparison between our results and those are available in the literature shows that the main results of this paper have new contributions to the related ones in the current literature. Two numerical examples are given to show the applications of the given results.
کلیدواژه‌ها
SDDEs؛ Second order؛ Multiple constant delays؛ Stability؛ Boundedness؛ Ito formula؛ LKF
مراجع
  • [1] A. M. A. Abou-El-Ela, A. I. Sadek, and A. M. Mahmoud, On the stability of solutions for certain second-order stochastic delay differential equations, Differ. Uravn. Protsessy Upr., 2 (2015), 1-13.
  • [2] A. M. A. Abou-El-Ela, A. I. Sadek, A. M. Mahmoud, and R. O. A. Taie, On the stochastic stability and boundedness of solutions for stochastic delay differential equation of the second order, Chin.J. Math. (N.Y.) 2015, Art. ID 358936, 8 PP.
  • [3] A. M. A. Abou-El-Ela, A. R. Sadek, A. M. Mahmoud, and E.S. Farghaly,  Asymptotic stability of solutions for  a certain non-autonomous second-order stochastic delay differential equation, Turkish J. Math., 41(3) (2017), 576-584.
  • [4] A.T. Ademola, S. O. Akindeinde, M. O. Ogundiran, and O. A. Adesina, On the stability and boundedness of solutions to certain second order nonlinear stochastic delay differential equations, J. Nigerian Math.  Soc.,  38(2) (2019), 185-209.
  • [5] A. T. Ademola, S. Moyo, B. S. Ogundare, M. O. Ogundiran, and O. A. Adesina, Stability and boundedness of solutions to a certain second-order nonautonomous stochastic differential equation, Int. J. Anal. 2016, Art. ID 2012315, 11 PP.
  • [6] O. A. Adesina, A. T. Ademola, M. O. Ogundiran, and B. S. Ogundare, Stability, boundedness and unique globel so- lutions to certain second order nonlinear stochastic delay differential equations with multiple deviating arguments, Nonlinear Stud. 26(1) (2019), 71-94.
  • [7] L. Arnold, Stochastic differential equations: Theory and applications, Jhon Wiley & Sons, 1974.
  • [8] J. Bao, G. Yin, and C. Yuan, Asymptotic analysis  for  functional  stochastic  differential  equation, Springer Bringer  in Mathematics. Springer, Cham, 2016.
  • [9] L. Huang and F. Deng, Razumikhin-type theorems on stability of neutral stochascit funcctional  differential  equa-  tions. IEEE Trans. Automat. Control, 7 (2008), 1718-1723.
  • [10] A.G. Ladde and G. S. Ladde, An introduction to differentianl equations.Vol.2.Stochastic modeling, methods and analysis, World Scientific Publishing Co. Pte.Ltd., Hackensack, NJ, 2013.
  • [11] J. Lei and M.C. Mackey, Stochastic differential delay equation, moment stability, and  application  to  hematopoietic stem cell regulation system. SIAM J.Appl.Math., 2 (2006/07), 387-407.
  • [12] K. Liu, Stability of infinite dimensional stochastic differential equations with applications, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, 135. Chapman & Hall/CRC, Boca Raton, FL, 2006.
  • [13] A. M. Mahmoud and C. Tun¸c, Stability and ultimate boundedness for non-autonomous system with variable delay, Appl. Math. Inf. Sci., 3 (2020), 431-440.
  • [14] X. Mao, Some contributions to stochastic asymptotic stability and boundedness via multiple Lyapunov functions. J. Math. Anal. Appl., 2 (2001), 325-340.
  • [15] X. Mao, Attraction, stability and boundedness for stochastic differential delay equations. Proceedings of the Third World Congress of Nonlinear Analysts, Part 7 (Catania, 2000). Nonlinear Anal., 7 (2001), 4795-4806.
  • [16] X. Mao, Stochastic differential equations and applications, Second edition. Horwood Publishing Limited, Chich-ester, 2008.
  • [17] S. E. A. Mohammed, Stochastic functional differential equations, Research Notes in Mathematics, 99. Pitman (Advanced Publishing Program), Boston, MA, 1984.
  • [18] A.  M.  Mahmoud  and  C.  Tun¸c,  Asymptotic  stability  of  solutions  for  a  kind  of  third-order  stochastic  differential equations with delays, Miscolc Math. Notes, 1(2019), 381-393.
  • [19] P. H. A. Ngoc, Explicit criteria for mean  square exponential stability of stochastic linear differential equations  with distributed delays. Wietnam J. Math., 1 (2020), 159-169.
  • [20] H. W. Rong and T. Fang, Asymptotic stability of second-order linear stochastic differential equations, Chinese J. Appl. Mech., 3 (1996), 72-78.
  • [21] L. Shaikhet, Lyapunov functionals and stability of stochastic functional differential equations, Springer, Cham, 2013.
  • [22] C. Tun¸c, Some new stability and boundedness results on the solutions of the nonlinear vector differential equations of second order, Iran. J. Sci. Technol. Trans. A Sci., 2 (2006), 213-221.
  • [23] C. Tun¸c,Boundedness results for solutions of certain nonlinear differential equations of second order, J. Indones. Math. Soc., 2 (2010), 115-126.
  • [24] C. Tun¸c, Stability and boundedness of solutions of nonautonomous differential equations of second order, J. Com- put. Anal. Appl., 6 (2011), 1067-1074.
  • [25] C.  Tun¸c,  Stability  and  uniform  boundedness  results  for  non-autonomous  Lineard-type  equations  with  a  variable deviating argument, Acta Math. Vietnam., 3 (2012), 311-325.
  • [26] C.  Tun¸c,  On  the  stability  and  boundedness  of  solutions  of  a  class  of  Lienard  equations  with  multiple  deviating arguments, Vietnam J. Math., 2 (2011), 177-190.
  • [27] C. Tun¸c, A note on boudedness of solutions to a class of non-autonomous differential equations of second order, Appl. Anal. Discrete Math. , 4(2) (2010), 361-372.
  • [28] C. Tun¸c, New stability and boundedness results of Lienard type equations with multiple deviating arguments, Izv. Nats. Akad. Nauk Armenii Mat. 45 (2010), no. 4, 47-56; reprinted in J. Contemp. Math. Anal., 4 (2010), 214-220.
  • [29] C.  Tun¸c,  Stability  to  vector  Lienard  equation  with  constand  deviating  argument,  Nonlinear  Dynam.,  3  (2013), 1245-1251.
  • [30] C. Tun¸c, A note on the bounded solutions to xII + c(t, x, xI) + b(t)f (x) = q(t), Appl. Math. Inf. Sci., 8(1) (2014), 393-399.
  • [31] C. Tun¸c,  Some  new  stability  and  boundedness  results  of  solutions  of  Lienard  type  equations  with  deviating  argu- ment, Nonlinear Anal. Hybrid Syst., 4(1) (2010), 85-91.
  • [32] C. Tun¸c, Stability and boundedness of solutions of nonautonomous differential equations of second order, J. Com- put. Anal. Appl. 13, 6 (2011), 1067-1074.
  • [33] C. Tun¸c, Uniformly stability and boundedness of solutions of second order nonlinear delay differential equations, Appl. Comput. Math. 10, 3 (2011), 449-462.
  • [34] C.  Tun¸c,  On  the  properties  of  solutions  for  a  system  of  non-linear  differential  equations  of  second  order,  Int.  J. Math. Comput. Sci.,2 (2019), 519-534.
  • [35] C. Tun¸c, On the qualitative behaviors of a functional differential equation of second order, Appl. Appl. Math., 2 (2017), 813-842.
  • [36] C. Tun¸c and T. Ayhan, On the asymptotic behavior of solutions to nonlinear differential equations of the second order, Comment. Math., 1 (2015), 1-8.
  • [37] C.  Tun¸c  and  E.  Tun¸c,  On  the  asymptotic  behavior  of  solutions  of  certain  second-order  differential  equations,  J. Franklin Inst., 5 (2007), 391-398.
  • [38] C.  Tun¸c  and  Y.  Din¸c,  Qualitative  properties  of  certain  nonlinear  differential  systems  of  second  order,  J.  Taibah Univ. Sci., 11(2) (2017), 359-366.
  • [39] C.  Tun¸c,  H.  S¸evli,  Stability  and  boudedness  properties  of  certain  second-order  differential  equations,  J.  Franklin Inst. 344, 5 (2007), 399-405.
  • [40] C.  Tun¸c  and  S.  Erdur,  New  qualitative  results  for  solutions  of  functional  differential  equations  of  second  order, Discrete Dyn. Nat. Soc., (2018), Art. ID 3151742, 13 pp.
  • [41] C. Tun¸c and O. Tun¸c, On the asymptotic stability of solutions of stochastic differential delay equations of second order, J. Taibah Univ. Sci. 13, 1 (2019), 875-882.
  • [42] C. Tun¸c and O. Tun¸c, On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order, J. Adv. Res., 7(1) (2016), 165-168.
  • [43] C. Tun¸c and O. Tun¸c,  A  note  on  the  stability  and  boundedness  of  solutions  to  non-linear  differential  systems  of second order, J. Assoc. Arab. Univ. Basic. Appl. Sci., 24 (2017), 169-175.
  • [44] C. Tun¸c and O. Tun¸c, A note on certain qualitative properties of a second order linear differential system, Appl. Math. Inf. Sci., 9(2) (2015), 953-956.
  • [45] R. Q. Wu and X. Mao, Existence and uniqueness of the solutions of stochastic differential equations, Stochastics, 11(1-2) (1983), 19-32.
  • [46] E. I. Verriest and P. Florchinger, Stability of stochastic systems with uncertain time delays, Syst Control Lett., 24(1) (1995), 41-47.
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