A new generalization of the y-function applied to model the anomalous diffusion-Reference-Cited by-同舟云学术

A new generalization of the y-function applied to model the anomalous diffusion

Published:2022 Issue:2 Part A Volume:26 Page:1069-1079
ISSN:0354-9836
Container-title:Thermal Science
language:en
Short-container-title:THERM SCI

Author:

Yang Xiao-Jun¹,Yu Xiao-Jin²

Affiliation:

1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, China + School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China

2. School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China

Abstract

In this paper, we propose the W-, K-, ?-, U-, V-, and O-functions for the first time. The K series representations for the W-, ?-, U-, V-, and O-functions are discussed. The derivatives, and integral transforms and special cases for the obtained special functions are presented. The anomalous diffusion models via derivative operators associated with the ?- and L-functions are suggested. The obtained results are used to give the series representations for the I-, H-, and G-functions.

Publisher

National Library of Serbia

Subject

Renewable Energy, Sustainability and the Environment

Reference8 articles.

1. Yang, X.-J., The Y-Function Applied in the Study of an Anomalous Diffusion, Thermal Science, 25 (2021), 6B, pp. 4465-4475

2. Fox, C., The G- and H-Functions as Symmetrical Fourier Kernels, Transactions of the American Mathematical Society, 98 (1961), 3, pp. 395-429

3. Meijer, C. S., Über Whittakersche bzw Besselsche Funktionen und Deren Produkte, Nieuw Archief voor Wiskunde, 18 (1936), 2, pp. 10-29

4. Rathie, A. K., A New Generalization of Generalized Hypergeometric Functions, Le Matematiche, 52 (1997), 2, pp. 297-310

5. Inayat-Hussain, A. A., New Properties of Hypergeometric Series Derivable from Feynman Integrals II, A Generalisation of the H Function, Journal of Physics A, 20 (1987), 13, pp. 4119-4128

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