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A new operational matrix based on Müntz–Legendre polynomials for solving distributed order fractional differential equations

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  • Pourbabaee, Marzieh
  • Saadatmandi, Abbas

Abstract

Our main aim in this work is to find the operational matrix of fractional derivative and the operational matrix of distributed order fractional derivative for the Müntz–Legendre polynomials (MLPs). The operational matrix approach with the tau method or collocation method is applied to reduce the solution of the linear/nonlinear distributed order fractional differential equations (DFDEs) to a system of linear/nonlinear algebraic equations. Moreover, seven numerical examples are included to show the validity and applicability of the suggested methods.

Suggested Citation

  • Pourbabaee, Marzieh & Saadatmandi, Abbas, 2022. "A new operational matrix based on Müntz–Legendre polynomials for solving distributed order fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 210-235.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:210-235
    DOI: 10.1016/j.matcom.2021.11.023
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    References listed on IDEAS

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    1. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2019. "A novel Legendre operational matrix for distributed order fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 215-231.
    2. Nastaran Ejlali & Seyed Mohammad Hosseini, 2017. "A Pseudospectral Method for Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 83-107, July.
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    Cited by:

    1. Marzban, Hamid Reza, 2022. "A generalization of Müntz-Legendre polynomials and its implementation in optimal control of nonlinear fractional delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Yang, Changqing, 2023. "Improved spectral deferred correction methods for fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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