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The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations

Author

Listed:
  • Haifa Bin Jebreen

    (Department of mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Ioannis Dassios

    (Faculty of Engineering, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece)

Abstract

The Chebyshev cardinal functions based on the Lobatto grid are introduced and used for the first time to solve the fractional delay differential equations. The presented algorithm is based on the collocation method, which is applied to solve the corresponding Volterra integral equation of the given equation. In the employed method, the derivative and fractional integral operators are expressed in the Chebyshev cardinal functions, which reduce the computational load. The method is characterized by its simplicity, adherence to boundary conditions, and high accuracy. An exact analysis has been provided to demonstrate the convergence of the scheme, and illustrative examples validate our investigation.

Suggested Citation

  • Haifa Bin Jebreen & Ioannis Dassios, 2024. "The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations," Mathematics, MDPI, vol. 12(21), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3388-:d:1509759
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    References listed on IDEAS

    as
    1. Amin, Rohul & Shah, Kamal & Asif, Muhammad & Khan, Imran, 2021. "A computational algorithm for the numerical solution of fractional order delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    2. Davis, L.C., 2003. "Modifications of the optimal velocity traffic model to include delay due to driver reaction time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 557-567.
    3. Samad Noeiaghdam & Denis Sidorov & Abdul-Majid Wazwaz & Nikolai Sidorov & Valery Sizikov, 2021. "The Numerical Validation of the Adomian Decomposition Method for Solving Volterra Integral Equation with Discontinuous Kernels Using the CESTAC Method," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
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