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Solving fractional pantograph delay differential equations via fractional-order Boubaker polynomials

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Abstract

In the current study, we introduce fractional-order Boubaker polynomials related to the Boubaker polynomials to achieve the numerical result for pantograph differential equations of fractional order in any arbitrary interval. The features of these polynomials are exploited to construct the new fractional integration and pantograph operational matrices. Then these matrices and least square approximation method are used to reorganize the problem to a nonlinear equations system which can be resolved by means of the Newton’s iterative method. The brief discussion about errors of the used estimations is deliberated and, finally, some examples are included to demonstrate the validity and applicability of our method.

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Acknowledgements

We express our appreciation to the reviewers for their helpful comments, which improved the quality of this work.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

    Kobra Rabiei & Yadollah Ordokhani

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  1. Kobra Rabiei
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  2. Yadollah Ordokhani
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Correspondence to Yadollah Ordokhani.

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Rabiei, K., Ordokhani, Y. Solving fractional pantograph delay differential equations via fractional-order Boubaker polynomials. Engineering with Computers 35, 1431–1441 (2019). https://doi.org/10.1007/s00366-018-0673-8

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