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A spectral shifted gegenbauer collocation method for fractional pantograph partial differential equations and its error analysis

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Abstract

This study presents a new numerical approach for solving fractional-order pantograph partial-differential equations, in which the fractional derivatives are expressed in the Caputo sense. New operational matrices are obtained by introducing the two-variable Gegenbauer polynomials. Using these matrices with the collocation method, solving the fractional order pantograph partial differential equation is converted into solving a system of algebraic equations. An error bound is computed for this method. Also, some examples are presented that show our proposed method has a better agreement with the exact solution in comparison with methods such as the homotopy perturbation and natural decomposition methods so that we can say that it is about \(10^{3}\) times more precise than the two mentioned methods. In general, our method provides a useful tool for solving these equations.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41938-19141, Rasht, Iran

    S Yaghoubi & H Aminikhah

  2. Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, P.O. Box 41938-19141, Rasht, Iran

    H Aminikhah

  3. Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia, 99138, Turkey

    K Sadri

  4. Mathematics Research Center, Near East University TRNC, Mersin 10, Nicosia, 99138, Turkey

    K Sadri

Authors
  1. S Yaghoubi
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  2. H Aminikhah
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  3. K Sadri
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Correspondence to H Aminikhah.

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Yaghoubi, S., Aminikhah, H. & Sadri, K. A spectral shifted gegenbauer collocation method for fractional pantograph partial differential equations and its error analysis. Sādhanā 48, 213 (2023). https://doi.org/10.1007/s12046-023-02270-5

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  • DOI: https://doi.org/10.1007/s12046-023-02270-5

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