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New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions

Author

Listed:
  • Weam Alharbi

    (Department of Mathematics, Faculty of Sciences, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Snezhana Hristova

    (Faculty of Mathematics and Informatics, Plovdiv University, Tzar Asen 24, 4000 Plovdiv, Bulgaria)

Abstract

The fractional generalization of the Ambartsumian delay equation with Caputo’s fractional derivative is considered. The Ambartsumian delay equation is very difficult to be solved neither in the case of ordinary derivatives nor in the case of fractional derivatives. In this paper we combine the Laplace transform with the Adomian decomposition method to solve the studied equation. The exact solution is obtained as a series which terms are expressed by the Mittag-Leffler functions. The advantage of the present approach over the known in the literature ones is discussed.

Suggested Citation

  • Weam Alharbi & Snezhana Hristova, 2021. "New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions," Mathematics, MDPI, vol. 9(2), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:157-:d:479774
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    References listed on IDEAS

    as
    1. Sayed M. Khaled & Essam R. El-Zahar & Abdelhalim Ebaid, 2019. "Solution of Ambartsumian Delay Differential Equation with Conformable Derivative," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
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