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The Wright Functions of the Second Kind in Mathematical Physics
Please always quote using this URN: urn:nbn:de:bvb:20-opus-207782
- In this review paper, we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics. We first start with the analytical properties of the classical Wright functions of which we distinguish two kinds. We then justify the relevance of the Wright functions of the second kind as fundamental solutions of the time-fractional diffusion-wave equations. Indeed, we think that this approach is the most accessible point of view for describing non-Gaussian stochastic processes and theIn this review paper, we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics. We first start with the analytical properties of the classical Wright functions of which we distinguish two kinds. We then justify the relevance of the Wright functions of the second kind as fundamental solutions of the time-fractional diffusion-wave equations. Indeed, we think that this approach is the most accessible point of view for describing non-Gaussian stochastic processes and the transition from sub-diffusion processes to wave propagation. Through the sections of the text and suitable appendices, we plan to address the reader in this pathway towards the applications of the Wright functions of the second kind.…
Author: | Francesco Mainardi, Armando Consiglio |
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URN: | urn:nbn:de:bvb:20-opus-207782 |
Document Type: | Journal article |
Faculties: | Fakultät für Physik und Astronomie / Institut für Theoretische Physik und Astrophysik |
Language: | English |
Parent Title (English): | Mathematics |
ISSN: | 2227-7390 |
Year of Completion: | 2020 |
Volume: | 8 |
Issue: | 6 |
Source: | Mathematics 2020, 8(6), 884; https://doi.org/10.3390/math8060884 |
DOI: | https://doi.org/10.3390/math8060884 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | Green’s functions; Laplace transform; Wright functions; diffusion-wave equation; fractional calculus |
Release Date: | 2021/12/23 |
Date of first Publication: | 2020/06/01 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |