대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권3호
  • /
  • Pages.967-982
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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HYERS-ULAM STABILITY OF FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH RANDOM IMPULSE

  • Dumitru Baleanu (Department of Mathematics Cankaya University, Institute of Space Sciences, Department of Medical Research China Medical University Hospital China Medical University) ;
  • Banupriya Kandasamy (Department of Mathematics with Computer Applications PSG College of Arts and Science) ;
  • Ramkumar Kasinathan (Department of Mathematics with Computer Applications PSG College of Arts and Science) ;
  • Ravikumar Kasinathan (Department of Mathematics PSG College of Arts and Science) ;
  • Varshini Sandrasekaran (Department of Mathematics PSG College of Arts and Science, Sri Eshwar College of Engineering)
  • 투고 : 2022.08.04
  • 심사 : 2022.11.22
  • 발행 : 2023.07.31
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초록

The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.

키워드

과제정보

The authors would like to thank the reviewers for their constructive comments in upgrading the article.

참고문헌

  1. R. Agarwal, S. Hristova, and D. O'Regan, Non-Instantaneous Impulses in Differential Equations, Springer, Cham, 2017. https://doi.org/10.1007/978-3-319-66384-5
  2. A. Ahmadova and N. I. Mahmudov, Existence and uniqueness results for a class of fractional stochastic neutral differential equations, Chaos Solitons Fractals 139 (2020), 110253, 8 pp. https://doi.org/10.1016/j.chaos.2020.110253
  3. S. Andr'as and A. R. M'esz'aros, Ulam-Hyers stability of elliptic partial differential equations in Sobolev spaces, Appl. Math. Comput. 229 (2014), 131-138. https://doi.org/10.1016/j.amc.2013.12.021
  4. A. Anguraj, K. Ramkumar, and K. Ravikumar, Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays, Comput. Methods Differ. Equ. 10 (2022), no. 1, 191-199.
  5. A. Anguraj and A. Vinodkumar, Existence and uniqueness of neutral functional differential equations with random impulses, Int. J. Nonlinear Sci. 8 (2009), no. 4, 412-418.
  6. A. Anguraj and A. Vinodkumar, Existence, uniqueness and stability results of random impulsive semilinear differential systems, Nonlinear Anal. Hybrid Syst. 4 (2010), no. 3, 475-483. https://doi.org/10.1016/j.nahs.2009.11.004
  7. E. Gselmann, Stability properties in some classes of second order partial differential equations, Results Math. 65 (2014), no. 1-2, 95-103. https://doi.org/10.1007/s00025-013-0332-8
  8. J. Huang, S.-M. Jung, and Y. Li, On Hyers-Ulam stability of nonlinear differential equations, Bull. Korean Math. Soc. 52 (2015), no. 2, 685-697. https://doi.org/10.4134/BKMS.2015.52.2.685
  9. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  10. S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order. II, Appl. Math. Lett. 19 (2006), no. 9, 854-858. https://doi.org/10.1016/j.aml.2005.11.004
  11. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
  12. S. Li, L. Shu, X. Shu, and F. Xu, Existence and Hyers-Ulam stability of random impulsive stochastic functional differential equations with finite delays, Stochastics 91 (2019), no. 6, 857-872. https://doi.org/10.1080/17442508.2018.1551400
  13. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1993.
  14. I. Podlubny, Fractional differential equations, Mathematics in Science and Engineering, 198, Academic Press, Inc., San Diego, CA, 1999.
  15. B. Radhakrishnan, M. Tamilarasi, and P. Anukokila, Existence, uniqueness and stability results for semilinear integrodifferential non-local evolution equations with random impulse, Filomat 32 (2018), no. 19, 6615-6626. https://doi.org/10.2298/fil1819615r
  16. R. Raja, U. K. Raja, R. Samidurai, and A. Leelamani, Passitivity analysis for uncertain discrete-time stochastic BAM neutral networks with time-varying delays, Neutral Comput. Appl. 25 (2014), 751-766.
  17. S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York, 1960.
  18. A. Vinodkumar, M. Gowrisankar, and P. Mohankumar, Existence, uniqueness and stability of random impulsive neutral partial differential equations, J. Egyptian Math. Soc. 23 (2015), no. 1, 31-36. https://doi.org/10.1016/j.joems.2014.01.005
  19. A. Vinodkumar, K. Malar, M. Gowrisankar, and P. Mohankumar, Existence, uniqueness and stability of random impulsive fractional differential equations, Acta Math. Sci. Ser. B (Engl. Ed.) 36 (2016), no. 2, 428-442. https://doi.org/10.1016/S0252-9602(16)30010-8
  20. X. Wang, D. Luo, Z. Luo, and A. Zada, Ulam-Hyers stability of Caputo-type fractional stochastic differential equations with time delays, Math. Probl. Eng. 2021 (2021), Art. ID 5599206, 24 pp. https://doi.org/10.1155/2021/5599206
  21. S. J. Wu and B. Zhou, Existence and uniqueness of stochastic differential equations with random impulses and Markovian switching under non-Lipschitz conditions, Acta Math. Sin. (Engl. Ser.) 27 (2011), no. 3, 519-536. https://doi.org/10.1007/s10114-011-9753-z
  22. Y. Zhou, J. R. Wang, and L. Zhang, Basic Theory of Fractional Differential Equations, World scientific, Singapore, 2014.
  23. Q. Zhu, Stability analysis of stochastic delay differential equations with Levy noise, Systems Control Lett. 118 (2018), 62-68. https://doi.org/10.1016/j.sysconle.2018.05.015
  24. Q. Zhu and T. Huang, Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion, Systems Control Lett. 140 (2020), 104699, 9 pp. https://doi.org/10.1016/j.sysconle.2020.104699
  25. Q. Zhu and B. Song, Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays, Nonlinear Anal. Real World Appl. 12 (2011), no. 5, 2851-2860. https://doi.org/10.1016/j.nonrwa.2011.04.011