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Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator

Author

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  • Azamat Dzarakhohov

    (Department of Mathematics and Physics, Gorsky State Agrarian University, Kirov Str. 37, North Ossetia-Alania, 362040 Vladikavkaz, Russia)

  • Yuri Luchko

    (Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany)

  • Elina Shishkina

    (Department of Mathematical and Applied Analysis, Voronezh State University, Universitetskaya pl., 1, 394018 Voronezh, Russia
    Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), Pobedy Street, 85, 308015 Belgorod, Russia)

Abstract

In this paper, we consider fractional ordinary differential equations and the fractional Euler–Poisson–Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator. Using the technique of the Meijer integral transform and its modification, fundamental solutions to these equations are derived in terms of the Fox–Wright function, the Fox H-function, and their particular cases. We also provide some explicit formulas for the solutions to the corresponding initial-value problems in terms of the generalized convolutions introduced in this paper.

Suggested Citation

  • Azamat Dzarakhohov & Yuri Luchko & Elina Shishkina, 2021. "Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator," Mathematics, MDPI, vol. 9(13), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1484-:d:581312
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    References listed on IDEAS

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    1. Elina Shishkina & Sergey Sitnik, 2019. "A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type," Mathematics, MDPI, vol. 7(12), pages 1-21, December.
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    Cited by:

    1. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2023. "On spectral polar fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 636-663.
    2. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

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