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© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

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 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.

Details

Title
On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters
Author
Rogosin Sergei 1   VIAFID ORCID Logo  ; Giraldi Filippo 2   VIAFID ORCID Logo  ; Mainardi, Francesco 3   VIAFID ORCID Logo 

 Department of Economics, Belarusian State University, Nezavisimosti Ave. 4, 220030 Minsk, Belarus; [email protected] 
 Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II 39, 00186 Rome, Italy; [email protected], School of Chemistry and Physics, University of KwaZulu-Natal, Westville Campus, Durban 4000, South Africa 
 Department of Physics & Astronomy, University of Bologna, and INFN, Via Irnerio 46, 40126 Bologna, Italy 
First page
1980
Publication year
2025
Publication date
2025
Publisher
MDPI AG
e-ISSN
22277390
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
3223926516
Copyright
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.