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Operator Method for Constructing a Solution of a Class of Linear Differential Equations of Fractional Order

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Functional Analysis in Interdisciplinary Applications (FAIA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 216))

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Abstract

In the paper certain method for constructing exact solutions of a class of linear differential equations of fractional order is considered. Algorithms for constructing solutions of the explicit form are developed for homogeneous and inhomogeneous differential equations of fractional order. This method is based on construction of normalized systems associated with fractional differentiation operator . 0 - normalized and f - normalized systems are built concerning to the pair of operators connected with the considered equation. Using 0 - normalized systems, linearly independent solutions of the homogeneous equation are constructed. Similarly, with the help of f - normalized systems partial solutions of the inhomogeneous equation are built in the case, where the right side is a quasi-polynomial, analytic function and an arbitrary function from the class of continuous functions.

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Acknowledgements

This research is financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (0819/GF4). This publication is supported by the target program 0085/PTSF-14 from the Ministry of Science and Education of the Republic of Kazakhstan.

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, 125 Pushkin st., Almaty, 050010, Kazakhstan

    Batirkhan Kh. Turmetov

  2. Department of Mathematics, Akhmet Yasawi International Kazakh-Turkish University, Turkistan, 161200, Kazakhstan

    Batirkhan Kh. Turmetov

Authors
  1. Batirkhan Kh. Turmetov
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Correspondence to Batirkhan Kh. Turmetov .

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Editors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Tynysbek Sh. Kalmenov

  2. Department of Mechanics and Mathematics, Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan

    Erlan D. Nursultanov

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Makhmud A. Sadybekov

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Turmetov, B.K. (2017). Operator Method for Constructing a Solution of a Class of Linear Differential Equations of Fractional Order. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_17

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