On Symmetrical Sonin Kernels in Terms of Hypergeometric-Type Functions

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

Mathematics, 2024, vol. 12, issue 24, 1-18

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.

Keywords: Sonin kernels; symmetrical Sonin kernels; Laplace integral transform; hypergeometric functions; Horn functions; general fractional derivative; general fractional integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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