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

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  • 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
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    References listed on IDEAS

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    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. Saeed, Umer, 2017. "CAS Picard method for fractional nonlinear differential equation," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 102-112.
    3. 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.
    4. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    5. 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).
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    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).

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