International Scientific Journal

Authors of this Paper

External Links


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.
PAPER REVISED: 2020-08-12
PAPER ACCEPTED: 2020-11-21
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 6, PAGES [4577 - 4584]
  1. Yang, X. J., Theory and Applications of Special Functions for Scientists and Engineers, Springer Singapore, New York, USA, 2021
  2. Temme, N. M., Special Functions: An Introduction the Classical Functions of Mathematical Physics, John Wiley & Sons, New York, USA, 1996
  3. 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
  4. 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
  5. 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
  6. Yang, X. J., The Y Function Applied in the Study of an Anomalous Diffusion, Thermal Science, 25 (2021), 6B, pp. 4465-4475
  7. Fox, C., The G and H Functions as Symmetrical Fourier Kernels, Transactions of the American Mathematical Society, 98 (1961), 3, pp. 395-429
  8. Meijer, C. S., Über Whittakersche bzw. Besselsche Funktionen und deren Produkte (in German), Nieuw Archief voor Wiskunde, 18 (1936), 2, pp. 10-29
  9. Wright, E. M., The Asymptotic Expansion of the Generalized Hypergeometric Function, Journal of the London Mathematical Society, 1 (1935), 4, pp. 286-293
  10. Yang, X. J., An Introduction Hypergeometric, Supertrigonometric, and Superhyperbolic Functions, Academic Press, New York, USA, 2021
  11. 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
  12. Wiman, A., Über den Fundamentalsatz in der Teorie der Funktionen Ea(x) (in German), Acta Mathematica, 29 (1905), 1, pp. 191-201
  13. 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
  14. Kohlrausch, R., Theorie des elektrischen rckstandes in der leidener flasche (in Geramn), Annalen der Physik, 167 (1854), 2, pp. 179-214
  15. 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
  16. Bailey, W. N., Generalized Hypergeometric Series, The University Press, New York, USA, 1935
  17. Mathai, A. M., et al., The H-Function: Theory and Applications, Springer, New York, USA, 2009
  18. Brychkov, Y. A., et al., Handbook of Mellin Transforms, CRC Press, New York, USA, 2018
  19. Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197

© 2023 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