IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v146y2021ics0960077921002757.html
   My bibliography  Save this article

A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations

Author

Listed:
  • Hamid, Muhammad
  • Usman, Muhammad
  • Haq, Rizwan Ul
  • Tian, Zhenfu

Abstract

The study of complex nonlinear mathematical models of fractional-order needs more attention in recent decades due to its enormous contribution to science and technology. Herein, a combined algorithm is proposed using the Chelyshkov polynomial method (CPM) and Picard iterative (PI) scheme. The proposed Picard Chelyshkov polynomial method (PCPM) is used to attain nonlinear oscillatory problems of arbitrary orders that do not have the exact solutions in the literature. The PCPM covert the highly nonlinear fractional-order oscillatory Problems into a linear algebraic equations system. However, the Picard scheme is to tackle the nonlinearity factor that appears in the differential equations. The proposed method's performance is examined through some test problems of fractional order while authenticated via some numerical methods. A comprehensive comparative study discussed with published work to show that the presented PCPM. To summarize, a more efficient and accurate tool is found to inspect the solution of fractional-order highly nonlinear models.

Suggested Citation

  • Hamid, Muhammad & Usman, Muhammad & Haq, Rizwan Ul & Tian, Zhenfu, 2021. "A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002757
    DOI: 10.1016/j.chaos.2021.110921
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921002757
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110921?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. Meng, Zhijun & Yi, Mingxu & Huang, Jun & Song, Lei, 2018. "Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 454-464.
    2. Oğuz, Cem & Sezer, Mehmet, 2015. "Chelyshkov collocation method for a class of mixed functional integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 943-954.
    3. Hamid, Muhammad & Usman, Muhammad & Zubair, Tamour & Haq, Rizwan Ul & Shafee, Ahmad, 2019. "An efficient analysis for N-soliton, Lump and lump–kink solutions of time-fractional (2+1)-Kadomtsev–Petviashvili equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 528(C).
    4. Saeed, Umer, 2017. "CAS Picard method for fractional nonlinear differential equation," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 102-112.
    5. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    6. Edmundo Capelas de Oliveira & José António Tenreiro Machado, 2014. "A Review of Definitions for Fractional Derivatives and Integral," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giacomo Ascione & Enrica Pirozzi, 2021. "Generalized Fractional Calculus for Gompertz-Type Models," Mathematics, MDPI, vol. 9(17), pages 1-32, September.
    2. Fengkai Gao & Dongmin Yu & Qiang Sheng, 2022. "Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study," Mathematics, MDPI, vol. 10(9), pages 1-13, May.
    3. Dongmin Yu & Rijun Wang, 2022. "An Optimal Investigation of Convective Fluid Flow Suspended by Carbon Nanotubes and Thermal Radiation Impact," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    4. Hamid, Muhammad & Usman, Muhammad & Yan, Yaping & Tian, Zhenfu, 2022. "An efficient numerical scheme for fractional characterization of MHD fluid model," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Hamid, Muhammad & Usman, Muhammad & Yan, Yaping & Tian, Zhenfu, 2023. "A computational numerical algorithm for thermal characterization of fractional unsteady free convection flow in an open cavity," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

    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. Wang, Lei & Chen, Yi-Ming, 2020. "Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Naserizadeh, L. & Hadizadeh, M. & Amiraslani, A., 2021. "Cubature rules based on a bivariate degree-graded alternative orthogonal basis and their applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 231-245.
    3. Wang, Lei & Chen, Yiming & Cheng, Gang & Barrière, Thierry, 2020. "Numerical analysis of fractional partial differential equations applied to polymeric visco-elastic Euler-Bernoulli beam under quasi-static loads," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Torres-Hernandez, A. & Brambila-Paz, F. & Montufar-Chaveznava, R., 2022. "Acceleration of the order of convergence of a family of fractional fixed-point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    5. Shahid Saleem & Shahbaz Ahmad & Junseok Kim, 2023. "Total Fractional-Order Variation-Based Constraint Image Deblurring Problem," Mathematics, MDPI, vol. 11(13), pages 1-26, June.
    6. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.
    7. Sergio Adriani David & Carlos Alberto Valentim, 2015. "Fractional Euler-Lagrange Equations Applied to Oscillatory Systems," Mathematics, MDPI, vol. 3(2), pages 1-15, April.
    8. Kürkçü, Ömür Kıvanç & Aslan, Ersin & Sezer, Mehmet, 2016. "A numerical approach with error estimation to solve general integro-differential–difference equations using Dickson polynomials," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 324-339.
    9. Usman, Muhammad & Hamid, Muhammad & Khan, Zafar Hayat & Haq, Rizwan Ul, 2021. "Neuronal dynamics and electrophysiology fractional model: A modified wavelet approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    10. Balcı, Mehmet Ali & Sezer, Mehmet, 2016. "Hybrid Euler–Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 33-41.
    11. Ayşegül Daşcıoğlu & Serpil Salınan, 2019. "Comparison of the Orthogonal Polynomial Solutions for Fractional Integral Equations," Mathematics, MDPI, vol. 7(1), pages 1-10, January.
    12. Maria de Jesus Estudillo-Ayala & Hugo Aguirre-Ramos & Juan Gabriel Avina-Cervantes & Jorge Mario Cruz-Duarte & Ivan Cruz-Aceves & Jose Ruiz-Pinales, 2020. "Algorithmic Analysis of Vesselness and Blobness for Detecting Retinopathies Based on Fractional Gaussian Filters," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    13. Cao, Jiawei & Chen, Yiming & Wang, Yuanhui & Cheng, Gang & Barrière, Thierry, 2020. "Shifted Legendre polynomials algorithm used for the dynamic analysis of PMMA viscoelastic beam with an improved fractional model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Çayan, Seda & Özhan, B. Burak & Sezer, Mehmet, 2022. "A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    15. Duarte Valério & Manuel D. Ortigueira & António M. Lopes, 2022. "How Many Fractional Derivatives Are There?," Mathematics, MDPI, vol. 10(5), pages 1-18, February.
    16. Muhammad Ismail & Umer Saeed & Jehad Alzabut & Mujeeb ur Rehman, 2019. "Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method," Mathematics, MDPI, vol. 7(12), pages 1-20, December.
    17. Mohra Zayed & Mahmoud Abul-Ez & Mohamed Abdalla & Nasser Saad, 2020. "On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials," Mathematics, MDPI, vol. 8(1), pages 1-23, January.
    18. Soradi-Zeid, Samaneh & Jahanshahi, Hadi & Yousefpour, Amin & Bekiros, Stelios, 2020. "King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    19. Nikooeinejad, Z. & Heydari, M. & Loghmani, G.B., 2022. "A numerical iterative method for solving two-point BVPs in infinite-horizon nonzero-sum differential games: Economic applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 404-427.
    20. Atanacković, Teodor M. & Janev, Marko & Pilipović, Stevan, 2018. "Non-linear boundary value problems involving Caputo derivatives of complex fractional order," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 326-342.

    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:146:y:2021:i:c:s0960077921002757. 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.