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A numerical method to solve fractional pantograph differential equations with residual error analysis

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Abstract

In this study, we have introduced a fractional series solution method to solve fractional pantograph differential equations numerically. The method is constructed by collocation approach and Bernstein polynomials. Each term of the equation is converted into a matrix form by the fractional Bernstein series. Then, the problems are reduced into a set of algebraic equations including unknown Bernstein coefficients by using the collocation nodes. Hence, by determining the coefficients, the approximate solution is obtained. For the error analysis of this method, we give two techniques which estimate or bound the absolute error. To demonstrate the efficiency and applicability of the method, some illustrative examples are given. We also compare the method with some known methods in the literature.

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Acknowledgements

The authors are grateful to the referees and the editor for a careful checking of the details and for helpful comments that improved this paper.

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  1. Department of Mathematics, Faculty of Science, Mugla Sıtkı Koçman University, Mugla, 48000, Turkey

    Elcin Gokmen

  2. Elementary Mathematics Education Program, Faculty of Education, Mugla Sıtkı Koçman University, Mugla, 48000, Turkey

    Osman Raşit Isik

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  1. Elcin Gokmen
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Correspondence to Elcin Gokmen.

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Gokmen, E., Isik, O.R. A numerical method to solve fractional pantograph differential equations with residual error analysis. Math Sci 16, 361–371 (2022). https://doi.org/10.1007/s40096-021-00426-0

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