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Keywords = efros theorem

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14 pages, 263 KB  
Article
On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters
by Sergei Rogosin, Filippo Giraldi and Francesco Mainardi
Mathematics 2025, 13(12), 1980; https://doi.org/10.3390/math13121980 - 16 Jun 2025
Cited by 2 | Viewed by 1042
Abstract
This article is devoted to the derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag–Leffler-type, Wright, and Le Roy-type functions. These formulas show the interconnection of these functions and lead to a better [...] Read more.
This article is devoted to the derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag–Leffler-type, Wright, and Le Roy-type functions. These formulas show the interconnection of these functions and lead to a better understanding of their behavior on the real line. These formulas are represented in a convoluted form and reconstructed in a more suitable form by using the Efros theorem. Full article
(This article belongs to the Special Issue Fractional Differential Equations: Theory and Application)
15 pages, 400 KB  
Article
Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of sμ exp(−sν)
by Alexander Apelblat and Francesco Mainardi
Symmetry 2021, 13(2), 354; https://doi.org/10.3390/sym13020354 - 22 Feb 2021
Cited by 14 | Viewed by 3445
Abstract
Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly [...] Read more.
Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of sμexp(sν) with μ0 and 0<ν<1 are presented. Full article
(This article belongs to the Special Issue Special Functions and Polynomials)
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