IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p856-d362553.html
   My bibliography  Save this article

A New Proof of the Existence of Nonzero Weak Solutions of Impulsive Fractional Boundary Value Problems

Author

Listed:
  • Asma Alharbi

    (Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Buraidah 51452, Saudi Arabia
    These authors contributed equally to this work.)

  • Rafik Guefaifia

    (Department of Mathematics, Faculty of Exact Sciences, University Tebessa 12002, Tebessa 12002, Algeria
    These authors contributed equally to this work.)

  • Salah Boulaaras

    (Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Buraidah 51452, Saudi Arabia
    Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Benbella, Oran 31000, Algeria
    These authors contributed equally to this work.)

Abstract

The paper deals with the existence of at least two non zero weak solutions to a new class of impulsive fractional boundary value problems via Brezis and Nirenberg’s Linking Theorem. Finally, an example is presented to illustrate our results.

Suggested Citation

  • Asma Alharbi & Rafik Guefaifia & Salah Boulaaras, 2020. "A New Proof of the Existence of Nonzero Weak Solutions of Impulsive Fractional Boundary Value Problems," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:856-:d:362553
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/856/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/5/856/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chuanzhi Bai, 2012. "Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, September.
    2. James W. Kirchner & Xiahong Feng & Colin Neal, 2000. "Fractal stream chemistry and its implications for contaminant transport in catchments," Nature, Nature, vol. 403(6769), pages 524-527, February.
    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. Zhang, Jingyuan, 2018. "A stable explicitly solvable numerical method for the Riesz fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 209-227.
    2. Qu Simin & Wang Tao & Bao Weimin & Shi Peng & Jiang Peng & Zhou Minmin & Yu Zhongbo, 2013. "Evaluating Infiltration Mechanisms Using Breakthrough Curve and Mean Residence Time," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(13), pages 4579-4590, October.
    3. Reaney, Sim M. & Lane, Stuart N. & Heathwaite, A. Louise & Dugdale, Lucy J., 2011. "Risk-based modelling of diffuse land use impacts from rural landscapes upon salmonid fry abundance," Ecological Modelling, Elsevier, vol. 222(4), pages 1016-1029.
    4. Abdelkawy, M.A. & Alyami, S.A., 2021. "Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. Xie, Yingying & Yin, Daopeng & Mei, Liquan, 2022. "Finite difference scheme on graded meshes to the time-fractional neutron diffusion equation with non-smooth solutions," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    6. Treena Basu, 2015. "A Fast O ( N log N ) Finite Difference Method for the One-Dimensional Space-Fractional Diffusion Equation," Mathematics, MDPI, vol. 3(4), pages 1-13, October.
    7. Taohua Liu & Xiucao Yin & Yinghao Chen & Muzhou Hou, 2023. "A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation," Mathematics, MDPI, vol. 11(8), pages 1-15, April.
    8. Lv, Yujuan & Gao, Lei & Geris, Josie & Verrot, Lucile & Peng, Xinhua, 2018. "Assessment of water sources and their contributions to streamflow by end-member mixing analysis in a subtropical mixed agricultural catchment," Agricultural Water Management, Elsevier, vol. 203(C), pages 411-422.
    9. Samer S. Ezz-Eldien & Ramy M. Hafez & Ali H. Bhrawy & Dumitru Baleanu & Ahmed A. El-Kalaawy, 2017. "New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 295-320, July.
    10. Wang, Wansheng & Huang, Yi, 2023. "Analytical and numerical dissipativity for the space-fractional Allen–Cahn equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 80-96.
    11. Hart, Rob, 2003. "Dynamic pollution control--time lags and optimal restoration of marine ecosystems," Ecological Economics, Elsevier, vol. 47(1), pages 79-93, November.
    12. Stephen, Damian G. & Dixon, James A., 2011. "Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 160-168.
    13. Du, Qiang & Toniazzi, Lorenzo & Zhou, Zhi, 2020. "Stochastic representation of solution to nonlocal-in-time diffusion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2058-2085.

    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:gam:jmathe:v:8:y:2020:i:5:p:856-:d:362553. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.