THERMAL SCIENCE
International Scientific Journal
NEW INSIGHTS ON THE J AND Y FUNCTIONS IN THE HEAT TRANSFER
ABSTRACT
In this article, we propose the integral and differential operators within the kernel of the Y function for the first time. We study the properties of the J and Y functions. We also present the some new applications of the heat transfer and present the new representation for the solution of the heat equation in the 1-D case.
KEYWORDS
PAPER SUBMITTED: 2020-07-12
PAPER REVISED: 2020-08-12
PAPER ACCEPTED: 2020-11-21
PUBLISHED ONLINE: 2021-12-24
THERMAL SCIENCE YEAR
2021, VOLUME
25, ISSUE
Issue 6, PAGES [4577 - 4584]
- Yang, X. J., Theory and Applications of Special Functions for Scientists and Engineers, Springer Singapore, New York, USA, 2021
- Temme, N. M., Special Functions: An Introduction the Classical Functions of Mathematical Physics, John Wiley & Sons, New York, USA, 1996
- Łach, J., Pieczka, W., On the Properties of Some Special Functions Related to Bessel's Functions and Their Application in Heat Exchanger Theory, International Journal of Heat and Mass Transfer, 27 (1984), 12, pp. 2225-2238
- Gvozdenac, D., Analytical Solution of the Transient Response of Gas-to-Gas Crossflow Heat Exchanger with Both Fluids Unmixed, Journal of Heat Transfer, 108 (1986), 4, pp. 722-727
- Abro, K. A., et al., A Mathematical Study of Magnetohydrodynamic Casson Fluid Via Special Functions with Heat and Mass Transfer Embedded in Porous Plate, Malaysian Journal of Fundamental and Applied Sciences, 14 (2018), 1, pp. 52-58
- Yang, X. J., The Y Function Applied in the Study of an Anomalous Diffusion, Thermal Science, 25 (2021), 6B, pp. 4465-4475
- Fox, C., The G and H Functions as Symmetrical Fourier Kernels, Transactions of the American Mathematical Society, 98 (1961), 3, pp. 395-429
- Meijer, C. S., Über Whittakersche bzw. Besselsche Funktionen und deren Produkte (in German), Nieuw Archief voor Wiskunde, 18 (1936), 2, pp. 10-29
- Wright, E. M., The Asymptotic Expansion of the Generalized Hypergeometric Function, Journal of the London Mathematical Society, 1 (1935), 4, pp. 286-293
- Yang, X. J., An Introduction Hypergeometric, Supertrigonometric, and Superhyperbolic Functions, Academic Press, New York, USA, 2021
- 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
- Wiman, A., Über den Fundamentalsatz in der Teorie der Funktionen Ea(x) (in German), Acta Mathematica, 29 (1905), 1, pp. 191-201
- 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
- Kohlrausch, R., Theorie des elektrischen rckstandes in der leidener flasche (in Geramn), Annalen der Physik, 167 (1854), 2, pp. 179-214
- Williams, G., Watts D. C., Non-Symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function, Transactions of the Faraday society, 66 (1970), pp. 80-85
- Bailey, W. N., Generalized Hypergeometric Series, The University Press, New York, USA, 1935
- Mathai, A. M., et al., The H-Function: Theory and Applications, Springer, New York, USA, 2009
- Brychkov, Y. A., et al., Handbook of Mellin Transforms, CRC Press, New York, USA, 2018
- Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197