IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v160y2022ics0960077922004039.html
   My bibliography  Save this article

Solvability of pseudoparabolic equation with Caputo fractional derivative

Author

Listed:
  • Aitzhanov, S.E.
  • Kusherbayeva, U.R.
  • Bekenayeva, K.S.

Abstract

This paper is devoted to the study of solvability of the problem for a pseudo-parabolic equation with a Caputo fractional derivative. The existence of the weak solution is investigated by applying Galerkin approximations and a priori estimates. On the way to prove the weak solution's uniqueness of the problem the Sobolev embedding theorem, Rellich-Kondrashov theorem and Gronwall-Bellman Lemma are applied. Along with this, the blow up of the solution to the problem in finite time is proved. The global solvability of the initial boundary value problem and the uniqueness of the weak generalized solution have been studied.

Suggested Citation

  • Aitzhanov, S.E. & Kusherbayeva, U.R. & Bekenayeva, K.S., 2022. "Solvability of pseudoparabolic equation with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004039
    DOI: 10.1016/j.chaos.2022.112193
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922004039
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112193?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. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    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. Musrrat Ali & Hemant Gandhi & Amit Tomar & Dimple Singh, 2023. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    2. Xing, Sheng Yan & Lu, Jun Guo, 2009. "Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1163-1169.
    3. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Jehad Alzabut & Weerawat Sudsutad & Zeynep Kayar & Hamid Baghani, 2019. "A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
    8. Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
    9. Ning, Xin & Ma, Yanyan & Li, Shuai & Zhang, Jingmin & Li, Yifei, 2018. "Response of non-linear oscillator driven by fractional derivative term under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 102-107.
    10. Lashkarian, Elham & Reza Hejazi, S., 2017. "Group analysis of the time fractional generalized diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 572-579.
    11. Majumdar, Prahlad & Mondal, Bapin & Debnath, Surajit & Ghosh, Uttam, 2022. "Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    12. Maneesha Gupta & Richa Yadav, 2013. "Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts," Journal of Optimization, Hindawi, vol. 2013, pages 1-11, June.
    13. Erman, Sertaç & Demir, Ali, 2020. "On the construction and stability analysis of the solution of linear fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    14. Serik Aitzhanov & Kymbat Bekenayeva & Zamira Abdikalikova, 2023. "Boundary Value Problem for a Loaded Pseudoparabolic Equation with a Fractional Caputo Operator," Mathematics, MDPI, vol. 11(18), pages 1-12, September.
    15. Emadifar, Homan & Nonlaopon, Kamsing & Muhammad, Shoaib & Nuruddeen, Rahmatullah Ibrahim & Kim, Hwajoon & Ahmad, Abdulaziz Garba, 2023. "Analytical investigation of the coupled fractional models for immersed spheres and oscillatory pendulums," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    16. Trong, Dang Duc & Hai, Dinh Nguyen Duy & Minh, Nguyen Dang, 2019. "Optimal regularization for an unknown source of space-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 184-206.
    17. González-Calderón, Alfredo & Vivas-Cruz, Luis X. & Taneco-Hernández, M.A. & Gómez-Aguilar, J.F., 2023. "Assessment of the performance of the hyperbolic-NILT method to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 375-390.
    18. Ngounou, A.M. & Mba Feulefack, S.C. & Anague Tabejieu, L.M. & Nana Nbendjo, B.R., 2022. "Design, analysis and horseshoes chaos control on tension leg platform system with fractional nonlinear viscoelastic tendon force under regular sea wave excitation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    19. André Liemert & Alwin Kienle, 2016. "Fractional Schrödinger Equation in the Presence of the Linear Potential," Mathematics, MDPI, vol. 4(2), pages 1-14, May.
    20. Liu, Haiyu & Lü, Shujuan, 2019. "Galerkin spectral method for nonlinear time fractional Cable equation with smooth and nonsmooth solutions," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 32-47.

    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:160:y:2022:i:c:s0960077922004039. 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.