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AIMS Mathematics

2024, Volume 9, Issue 6: 15246-15262. doi: 10.3934/math.2024740
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Efficient spectral collocation method for nonlinear systems of fractional pantograph delay differential equations

  • 1.
    Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box-65892, Riyadh 11566, Saudi Arabia
  • 2.
    Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
  • 3.
    Art and Science Faculty, Department of Mathematics, Siirt University, 56100 Siirt, Turkey
  • 4.
    Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
  • 5.
    Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg 620002, Russia
  • Received: 09 March 2024 Revised: 22 April 2024 Accepted: 23 April 2024 Published: 28 April 2024

  • MSC : 26A33, 33D45, 65M70

  • Caputo-Hadamard-type fractional calculus involves the logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenges in numerical approximations. In this paper, we construct and analyze a spectral collocation approach using mapped Jacobi functions as basis functions and construct an efficient algorithm to solve systems of fractional pantograph delay differential equations involving Caputo-Hadamard fractional derivatives. What we study is the error estimates of the derived method. In addition, we tabulate numerical results to support our theoretical analysis.

    Citation: M. A. Zaky, M. Babatin, M. Hammad, A. Akgül, A. S. Hendy. Efficient spectral collocation method for nonlinear systems of fractional pantograph delay differential equations[J]. AIMS Mathematics, 2024, 9(6): 15246-15262. doi: 10.3934/math.2024740

    Related Papers:

  • Caputo-Hadamard-type fractional calculus involves the logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenges in numerical approximations. In this paper, we construct and analyze a spectral collocation approach using mapped Jacobi functions as basis functions and construct an efficient algorithm to solve systems of fractional pantograph delay differential equations involving Caputo-Hadamard fractional derivatives. What we study is the error estimates of the derived method. In addition, we tabulate numerical results to support our theoretical analysis.


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