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Efficient method for solving variable-order pantograph models

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Abstract

This paper shows how to solve variable-order pantograph-delay differential equations (VO-PDDEs) and variable-order pantograph Volterra delay integro-differential equations (VO-VDIDEs) using shifted fractional Gegenbauer operational matrices (SFGOMs) of differentiation and integration in conjunction with the spectral collocation method. In these equations, the fractional derivatives of variable order are represented in the Caputo sense. As a result of the proposed method, the considered problems are translated into an easy-to-solve system of algebraic equations. The proposed technique’s error bound is examined. To demonstrate the utility of the proposed method, numerical test problems are introduced and compared with other numerical methods in the existing literature.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Minia University, Minia, 61519, Egypt

    Hoda F Ahmed

  2. Department of Mathematics, Faculty of Science, New Valley University, Kharga, 72511, Egypt

    Marina B Melad

Authors
  1. Hoda F Ahmed
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  2. Marina B Melad
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Correspondence to Marina B Melad.

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Ahmed, H.F., Melad, M.B. Efficient method for solving variable-order pantograph models. Pramana - J Phys 95, 183 (2021). https://doi.org/10.1007/s12043-021-02218-6

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  • DOI: https://doi.org/10.1007/s12043-021-02218-6

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