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On Symmetrical Sonin Kernels in Terms of Hypergeometric-Type Functions

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  • Yuri Luchko

    (Department of Mathematics, Physics, and Chemistry, Berlin University of Applied Sciences and Technology, 13353 Berlin, Germany)

Abstract

In this paper, a new class of kernels of integral transforms of the Laplace convolution type that we named symmetrical Sonin kernels is introduced and investigated. For a symmetrical Sonin kernel given in terms of elementary or special functions, its associated kernel has the same form with possibly different parameter values. In the paper, several new kernels of this type are derived by means of the Sonin method in the time domain and using the Laplace integral transform in the frequency domain. Moreover, for the first time in the literature, a class of Sonin kernels in terms of the convolution series, which are a far-reaching generalization of the power series, is constructed. The new symmetrical Sonin kernels derived in the paper are represented in terms of the Wright function and the new special functions of the hypergeometric type that are extensions of the corresponding Horn functions in two variables.

Suggested Citation

  • Yuri Luchko, 2024. "On Symmetrical Sonin Kernels in Terms of Hypergeometric-Type Functions," Mathematics, MDPI, vol. 12(24), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3943-:d:1544226
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    References listed on IDEAS

    as
    1. Tarasov, Vasily E., 2023. "Nonlocal statistical mechanics: General fractional Liouville equations and their solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    2. Vasily E. Tarasov, 2021. "General Fractional Calculus: Multi-Kernel Approach," Mathematics, MDPI, vol. 9(13), pages 1-14, June.
    3. Stefan G. Samko & Rogério P. Cardoso, 2003. "Integral equations of the first kind of Sonine type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-24, January.
    4. Yuri Luchko & Masahiro Yamamoto, 2020. "The General Fractional Derivative and Related Fractional Differential Equations," Mathematics, MDPI, vol. 8(12), pages 1-20, November.
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