Academic Journal
New Extended Three-Variable Mittag-Leffler Type Functions
| Title: | New Extended Three-Variable Mittag-Leffler Type Functions |
|---|---|
| Authors: | Hasanov, A., Yuldashova, H.A. |
| Source: | Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, Vol 52, Iss 3, Pp 24-43 (2025) |
| Publisher Information: | KamGU by Vitus Bering, 2025. |
| Publication Year: | 2025 |
| Collection: | LCC:Science |
| Subject Terms: | extended mittag-leffler type function, hypergeometric function, special (or higher transcendental) function, lauricella function, integral representation, system of partial differential equation, one- and threedimensional laplace transform, riemann-liouville fractional integral, riemann-liouville fractional derivative, appell and kamp´e de f´e riet functions, srivastava-daoust hypergeoemetric function, oбобщенная функция типа миттаг-леффлера, гипергеометрическая функция, специальная (или высшая трансцендентная) функция, функция лауричеллы, интегральное представление, система дифференциальных уравнений в частных производных, одномерное и трехмерное преобразование лапласа, дробный интеграл римана-лиувилля, дробная производная римана-лиувилля, функции аппеля и кампе де ферьет, гипергеометрическая функция сриваставы-даусту, Science |
| Description: | This article presents a systematic investigation of a new class of Mittag-Leffler-type functions in three variables. These functions are a natural and significant extension of the classical Mittag-Leffler function, and are constructed to correspond analogously to the well-known Lauricella hypergeometric functions of three variables. Our study comprehensively explores the fundamental properties and analytical characteristics of these threevariable functions. A primary focus is the establishment of their precise interrelationships with other existing extensions and generalizations of the classical Mittag-Leffler function, thereby situating them within the broader landscape of special functions. Key analytical findings presented in this work include: The derivation of the exact three-dimensional regions of convergence for the series defining these functions. The formulation of elegant Euler-type integral representations, which provide a powerful tool for further analysis. A detailed exploration of their integral transforms, specifically the derivation of both one-dimensional and three-dimensional Laplace transforms.The examination of their intimate connections with fractional calculus, demonstrating their natural emergence as kernels and solutions in the context of the Riemann-Liouville fractional integral and differential operators. Furthermore, we delve into the associated differential equations, showing that these Mittag-Lefflertype functions serve as solutions to specific systems of partial differential equations. This work not only enriches the theory of special functions but also provides a robust mathematical framework for potential applications in fractional differential equations, anomalous diffusion, and other areas of mathematical physics. |
| Document Type: | article |
| File Description: | electronic resource |
| Language: | English Russian |
| ISSN: | 2079-6641 2079-665X |
| Relation: | https://krasec.ru/hasanov2025523en/; https://doaj.org/toc/2079-6641; https://doaj.org/toc/2079-665X |
| DOI: | 10.26117/2079-6641-2025-52-3-24-43 |
| Access URL: | https://doaj.org/article/1c3c6716d65c41349667ba89abc5bca6 |
| Accession Number: | edsdoj.1c3c6716d65c41349667ba89abc5bca6 |
| Database: | Directory of Open Access Journals |
| ISSN: | 20796641 2079665X |
|---|---|
| DOI: | 10.26117/2079-6641-2025-52-3-24-43 |