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Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation

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  • Heydari, M.H.
  • Razzaghi, M.
  • Rouzegar, J.

Abstract

In this work, a category of delay distributed-order time fractional fourth-order sub-diffusion equations is investigated. The Chebyshev cardinal polynomials (as a proper class of basis functions) are employed to make an appropriate methodology for these problems. To this end, some matrix relationships regarding the distributed-order fractional differentiation (in the Caputo kind) of these polynomials are extracted and applied in generating the desired approach. The provided method converts solving these problems into obtaining the solution of systems of algebraic equations. The reliability of the technique is evaluated by solving three examples.

Suggested Citation

  • Heydari, M.H. & Razzaghi, M. & Rouzegar, J., 2022. "Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922007019
    DOI: 10.1016/j.chaos.2022.112495
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    References listed on IDEAS

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    1. Heydari, M.H. & Razzaghi, M., 2021. "Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Heydari, M.H. & Atangana, A., 2019. "A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana–Baleanu–Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 339-348.
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    4. Nandal, Sarita & Narain Pandey, Dwijendra, 2020. "Numerical solution of non-linear fourth order fractional sub-diffusion wave equation with time delay," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    5. Vargas, Antonio M., 2022. "Finite difference method for solving fractional differential equations at irregular meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 204-216.
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