THERMAL SCIENCE

International Scientific Journal

Xiao-Jun YangORCID

,

Yu-Rong Fan

THE SERIES REPRESENTATIONS FOR THE J AND H FUNCTIONS APPLIED IN THE HEAT-DIFFUSION EQUATION

ABSTRACT
In this article the theory of the supertrigonometric and superhyperbolic functions associated with the J and H functions are proposed for the first time. The series representation for the heat-diffusion equations are also given by using the J and H functions. The results are efficient and accurate for the description for the solutions of the PDE in mathematical physics.
KEYWORDS
heat-diffusion equation, H function, superhyperbolic functions, J function, super trigonometric functions
PAPER SUBMITTED: 2021-05-13
PAPER REVISED: 2021-06-10
PAPER ACCEPTED: 2021-07-25
PUBLISHED ONLINE: 2021-12-24
DOI REFERENCE: https://doi.org/10.2298/TSCI2106631Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE No. 6, PAGES [4631 - 4642]
REFERENCES
[1] Andrews, G. E., Askey, R., Roy, R., Special Functions, Cambridge University Press, Cambridge, England, UK, 1999
[2] Wang, Z. X., Guo, D. R., Special Functions, World Scientific, London, UK, 1989
[3] Yang, X. J., Theory and Applications of Special Functions for Scientists and Engineers, Springer Singapore, New York, USA, 2021, 10.1007/978-981-33-6334-2
[4] Fox, C., The G and H functions as symmetrical Fourier kernels, Transactions of the American Mathematical Society, 98 (1961), 3, pp. 395-429, 10.2307/1993339
[5] Mathai, A. M., et al., The H-Function: Theory and Applications, Springer, New York, USA, 2009
[6] Yang, X.-J., The Y Function Applied in the Study of an Anomalous Diffusion, Thermal Science, 25 (2021), 6B, pp. 4465-4475, 10.2298/tsci2106465y
[7] Euler, L., Introductio in Analysin Infinitorum, Apud Marcum-Michaelem Bousquet & Socios, Bousquet, France, 1748
[8] Yang, X. J., An Introduction Hypergeometric, Supertrigonometric and Superhyperbolic Functions, Academic Press, New York, USA, 2021, 10.1016/c2020-0-01879-7
[9] Mittag-Leffler, G. M., Sur la nouvelle fonction Eα(x) (in French), Comptes Rendus de L'Academie des Sciences Paris, 137 (1903), 2, pp. 554-558
[10] Wiman, A., Über den Fundamentalsatz in der Teorie der Funktionen Ea(x) (in German), Acta Mathematica, 29 (1905), 1, pp. 191-201
[11] Prabhakar, T. R., A Singular Integral Equation with a Generalized Mittag Leffler Function in the Kernel, Yokohama Mathematical Journal, 19 (1971), 1, pp. 7-15
[12] Shukla, A. K., Prajapati, J. C., On a Generalization of Mittag-Leffler Function and Its Properties, Journal of Mathematical Analysis and Applications, 336 (2007), 2, pp. 797-811, 10.1016/j.jmaa.2007.03.018
[13] Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197, 10.1016/j.aml.2016.09.011
PDF VERSION [DOWNLOAD]
The series representations for the J and H functions applied in the heat-diffusion equation

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence