Fractional Pantograph Delay Equations Solving by the Meshless Methods

This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bern...

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Bibliographic Details
Published inIbn Al-Haitham Journal for Pure and Applied Sciences Vol. 36; no. 3; pp. 382 - 397
Main Authors M. N. Jasim, Shefaa, H. Ibraheem, Ghada
Format Journal Article
LanguageEnglish
Published University of Baghdad 20.07.2023
Subjects
Bernstein polynomials
Legendre polynomials
Pantograph Delay Equations
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Summary:This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bernstein polynomials and the operational matrix of the fractional derivative with Shifted Legendre polynomials. The basic procedure of this method is to convert the pantograph delay equation to a system of linear equations and by using, the operational matrices we get rid of the integration and differentiation operations, which makes solving the problem easier. The concept of Caputo has been used to describe fractional derivatives. Finally, some numerical examples are identified to show the utility and capability of the two proposed approaches. Mathematica®12 program has been relied upon in the calculations.
ISSN:1609-4042
2521-3407
DOI:10.30526/36.3.3076