• Efficient method for solving variable-order pantograph models

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    • Keywords


      Fractional pantograph delay differential equations with variable-order; fractional pantograph Volterra delay integro-differential equations with variable-order; shifted fractional Gegenbauer polynomials; operational matrices; collocation method.

    • 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 systemof 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 theexisting literature.

    • Author Affiliations



      1. Department of Mathematics, Faculty of Science, Minia University, Minia 61519, Egypt
      2. Department of Mathematics, Faculty of Science, New Valley University, Kharga 72511, Egypt
    • Dates

  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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