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Solving fractional-order delay integro-differential equations using operational matrix based on fractional-order Euler polynomials

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Abstract

In this paper, we present a numerical method to solve fractional-order delay integro-differential equations. We use the operational matrices based on the fractional-order Euler polynomials to obtain numerical solution of the considered equations. By approximating the unknown function and its derivative in terms of the fractional-order Euler polynomials and substituting these approximations into the original equation, the original equation is reduced to a system of nonlinear algebraic equations. The convergence analysis of the proposed method is discussed. Finally, some examples are included to show the accuracy and validity of the proposed method.

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Acknowledgements

The authors would like to express their gratitude for the referees of the paper for their valuable suggestions that improved the final form of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

    S. Rezabeyk

  2. Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran

    S. Abbasbandy & E. Shivanian

Authors
  1. S. Rezabeyk
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  2. S. Abbasbandy
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  3. E. Shivanian
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Correspondence to S. Abbasbandy.

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Rezabeyk, S., Abbasbandy, S. & Shivanian, E. Solving fractional-order delay integro-differential equations using operational matrix based on fractional-order Euler polynomials. Math Sci 14, 97–107 (2020). https://doi.org/10.1007/s40096-020-00320-1

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