IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v137y2020ics096007792030299x.html
   My bibliography  Save this article

Doubly-weighted pseudo almost automorphic solutions for stochastic dynamic equations with Stepanov-like coefficients on time scales

Author

Listed:
  • Dhama, Soniya
  • Abbas, Syed
  • Debbouche, Amar

Abstract

This manuscript introduces the square-mean doubly weighted pseudo almost automorphy and also square-mean doubly weighted pseudo almost automorphy in the sense of Stepanov (Sl2) over time scales. We derive results for a general stochastic dynamic system on time scales which can model a stochastic cellular neural network with time shifting delays on time scales. The coefficients are considered to be doubly weighted Stepanov-like pseudo almost automorphic functions in square-mean sense which is more general than weighted pseudo almost automorphic functions. We present several new and key results such as composition theorem for such functions on time scale. These results play a crucial role in order to study qualitative properties of nonlinear differential equations. Furthermore, we study the existence of a unique solution of stochastic delay cellular neural network on time scales. These results improve and extend the previous works in this direction. At the end, a numerical example is given to illustrate the analytical findings.

Suggested Citation

  • Dhama, Soniya & Abbas, Syed & Debbouche, Amar, 2020. "Doubly-weighted pseudo almost automorphic solutions for stochastic dynamic equations with Stepanov-like coefficients on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s096007792030299x
    DOI: 10.1016/j.chaos.2020.109899
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792030299X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109899?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Burgos, C. & Cortés, J.-C. & Debbouche, A. & Villafuerte, L. & Villanueva, R.-J., 2019. "Random fractional generalized Airy differential equations: A probabilistic analysis using mean square calculus," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 15-29.
    2. Kim, Hyunsoo & Sakthivel, Rathinasamy & Debbouche, Amar & Torres, Delfim F.M., 2020. "Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Wenqing Hu, 2017. "Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2017, pages 1-13, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akinlar, M.A. & Inc, Mustafa & Gómez-Aguilar, J.F. & Boutarfa, B., 2020. "Solutions of a disease model with fractional white noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. Ahmed, Hamdy M., 2022. "Construction controllability for conformable fractional stochastic evolution system with noninstantaneous impulse and nonlocal condition," Statistics & Probability Letters, Elsevier, vol. 190(C).
    3. Burgos, C. & Cortés, J.-C. & Villafuerte, L. & Villanueva, R.J., 2022. "Solving random fractional second-order linear equations via the mean square Laplace transform: Theory and statistical computing," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    4. Kim, Hyunsoo & Sakthivel, Rathinasamy & Debbouche, Amar & Torres, Delfim F.M., 2020. "Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Villafuerte, L., 2023. "Solution processes for second-order linear fractional differential equations with random inhomogeneous parts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 17-48.
    6. Zakaria Ali & Minyahil Abera Abebe & Talat Nazir, 2024. "Strong Convergence of Euler-Type Methods for Nonlinear Fractional Stochastic Differential Equations without Singular Kernel," Mathematics, MDPI, vol. 12(18), pages 1-36, September.
    7. Han, Tianyong & Li, Zhao & Shi, Kaibo & Wu, Guo-Cheng, 2022. "Bifurcation and traveling wave solutions of stochastic Manakov model with multiplicative white noise in birefringent fibers," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    8. Jornet, Marc, 2021. "Beyond the hypothesis of boundedness for the random coefficient of the Legendre differential equation with uncertainties," Applied Mathematics and Computation, Elsevier, vol. 391(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s096007792030299x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.