IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v147y2021ics0960077921003027.html
   My bibliography  Save this article

On the solvability and approximate solution of a one-dimensional singular problem for a p-Laplacian fractional differential equation

Author

Listed:
  • Jong, KumSong
  • Choi, HuiChol
  • Kim, MunChol
  • Kim, KwangHyok
  • Jo, SinHyok
  • Ri, Ok

Abstract

In this paper, using the monotone iterative technique, we discuss a new approximate method for solving multi-point boundary value problems of p-Laplacian fractional differential equations with singularities, which are of great importance in the fluid dynamics field. To do this, first, a sequence of auxiliary problems that release the nonlinear source terms contained in the equations from the singularities is set up, and the uniqueness and existence of their positive solutions are established. Next, we show the relative compactness of the sequence of unique solutions to these auxiliary problems to prove the solvability of our given problem. And we present some sufficient conditions to construct a sequence of approximate solutions that converges to an exact solution of our problem. Finally, we give two numerical examples to demonstrate our main results.

Suggested Citation

  • Jong, KumSong & Choi, HuiChol & Kim, MunChol & Kim, KwangHyok & Jo, SinHyok & Ri, Ok, 2021. "On the solvability and approximate solution of a one-dimensional singular problem for a p-Laplacian fractional differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003027
    DOI: 10.1016/j.chaos.2021.110948
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921003027
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110948?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. Fang Wang & Lishan Liu & Yonghong Wu & Yumei Zou, 2019. "Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p -Laplacian Operator," Complexity, Hindawi, vol. 2019, pages 1-21, October.
    2. Škovránek, Tomáš & Podlubny, Igor & Petráš, Ivo, 2012. "Modeling of the national economies in state-space: A fractional calculus approach," Economic Modelling, Elsevier, vol. 29(4), pages 1322-1327.
    3. Abdulhameed, M. & Vieru, D. & Roslan, R., 2017. "Modeling electro-magneto-hydrodynamic thermo-fluidic transport of biofluids with new trend of fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 233-252.
    4. Wang, Fang & Liu, Lishan & Wu, Yonghong, 2020. "A numerical algorithm for a class of fractional BVPs with p-Laplacian operator and singularity-the convergence and dependence analysis," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    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. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    2. Maiti, S. & Shaw, S. & Shit, G.C., 2020. "Caputo–Fabrizio fractional order model on MHD blood flow with heat and mass transfer through a porous vessel in the presence of thermal radiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
    4. Michal Fečkan & JinRong Wang, 2017. "Mixed Order Fractional Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-9, November.
    5. Lu, Qinyun & Zhu, Yuanguo, 2021. "LQ optimal control of fractional-order discrete-time uncertain systems," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    6. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
    7. Llibre, Jaume & Valls, Clàudia, 2018. "On the global dynamics of a finance model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 1-4.
    8. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    9. Hao Ming & JinRong Wang & Michal Fečkan, 2019. "The Application of Fractional Calculus in Chinese Economic Growth Models," Mathematics, MDPI, vol. 7(8), pages 1-6, July.
    10. Svenkeson, A. & Beig, M.T. & Turalska, M. & West, B.J. & Grigolini, P., 2013. "Fractional trajectories: Decorrelation versus friction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5663-5672.
    11. Benito Chen-Charpentier & Gilberto González-Parra & Abraham J. Arenas, 2016. "Fractional Order Financial Models for Awareness and Trial Advertising Decisions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 555-568, December.
    12. Tomas Skovranek, 2019. "The Mittag-Leffler Fitting of the Phillips Curve," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    13. Ahmed Alsaedi & Rodica Luca & Bashir Ahmad, 2020. "Existence of Positive Solutions for a System of Singular Fractional Boundary Value Problems with p -Laplacian Operators," Mathematics, MDPI, vol. 8(11), pages 1-18, October.
    14. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Concept of dynamic memory in economics," Papers 1712.09088, arXiv.org.
    15. Ertuğrul Karaçuha & Vasil Tabatadze & Kamil Karaçuha & Nisa Özge Önal & Esra Ergün, 2020. "Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    16. Gani Stamov & Ivanka Stamova, 2019. "Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds," Mathematics, MDPI, vol. 7(11), pages 1-15, October.
    17. Tarasova, Valentina V. & Tarasov, Vasily E., 2017. "Logistic map with memory from economic model," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 84-91.
    18. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 520-531.
    19. Inés Tejado & Emiliano Pérez & Duarte Valério, 2020. "Fractional Derivatives for Economic Growth Modelling of the Group of Twenty: Application to Prediction," Mathematics, MDPI, vol. 8(1), pages 1-21, January.
    20. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.

    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:147:y:2021:i:c:s0960077921003027. 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.