A NOTE ON NATURAL TRANSFORMATION OF MORE GENERALIZED HYPERGEOMETRIC FUNCTION

Authors

  • Sheeraz Ali Sri Satya Sai University of technology and Medical Sciences Department of Mathematics (SSSUTM)
  • Farooq Ahmad Department of Mathematics Govt. College for Women Nawakadal. J&K
  • D. K. Jain Department of Engineering Mathematics & Computing Madhav Institute of Technology and Science. Gwalior (M.P.) India
  • Dr. syed shahnawaz Ali Department of Mathematics Sri satya sai University of technology and Medical Sciences

DOI:

https://doi.org/10.17605/OSF.IO/EXUAG

Keywords:

R-function, S-Function, Natural transform, Riemann Liouville fractional Integrals, Mittag-Leffler Function

Abstract

The objective of this paper is to investigate natural transform of the more generalized Hypergeometric function (R –function  & S- Function )   introduced by Hartley and Lorenzo [4] in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties in terms of Mittag-Leffler functions. Further, we show some applications of these natural transform in classical equations of mathematical physics, like the heat and the free electron laser equations, and in difference-differential equations governing the dynamics of generalized renewal stochastic processes.

Downloads

Download data is not yet available.

References

Belgacem, F. B. M. Applications of Sumudu transform to indefinite periodic parabolic equations. Proceedings of the 6th International Conference on Mathematical Problems & Aerospace Sciences, (ICNPAA 06), Chap. 6, pp 51-60,Cambridge Scientific Publishers, Cambridge, UK, 2007.

Belgacem, F. B. M. Sumudu transform applications to Bessel’s Functions and Equations. Applied Mathematical Sciences. Vol. 4. No. 74. pp 3665-3686. 2010.

Belgacem, F. B. M and Silambarasan, R. Theory of the Natural transform. Mathematics in Engg Sci and Aerospace (MESA) journal. Vol. 3. No. 1. pp 99-124. 2012.

R. K. Saxena, J. Daiya, Integral transforms of the S -function, Le Mathematiche, 70 (2015), 147–159.

Khan, Z. H. and Khan, W. A. N-transform properties and applications. NUST Jour. of Engg. Sciences. Vol. 1. No. 1. pp 127-133. 2008.

D. G. Duffy, Transform methods for solving partial differential equations, Second edition, Chapman & Hall/CRC, BocaRaton, FL, (2004).

T. A. Estrin, T. J. Higgins, The solution of boundary value problems by multiple Laplace transformations, J. Franklin Inst., 252 (1951), 153–167

M. R. Spiegel, Schaum’s outline of theory and problems of Laplace transforms, McGraw-Hill, New York, (1965).

Y. A. Brychkov, H.-J. Glaeske, A. P. Prudnikov, V˜u Kim Tuˆan, Multidimensional integral transformations, Gordon and Breach Science Publishers, Philadelphia, PA, (1992).

H. Eltayeb, A. Kılıc¸man, A note on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform, Appl. Math. Lett., 21 (2008), 1324–1329.

G. K. Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Internat. J. Math. Ed. Sci. Tech., 24 (1993), 35–43.

Y. A. Brychkov, H.-J. Glaeske, A. P. Prudnikov, V˜u Kim Tuˆan, Multidimensional integral transformations, Gordon and Breach Science Publishers, Philadelphia, PA, (1992).

A. Kılıc¸man, H. E. Gadain, On the applications of Laplace and Sumudu transforms, J. Franklin Inst., 347 (2010), 848–862.

G. K. Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Internat. J. Math. Ed. Sci. Tech., 24 (1993), 35–43. 1

A. Kılıc¸man, H. Eltayeb, On a new integral transform and differential equations, Math. Probl. Eng., 2010 (2010), 13 pages.

Downloads

Published

22-10-2021

How to Cite

[1]
Sheeraz Ali, Farooq Ahmad, D. K. Jain, and Dr. syed shahnawaz Ali, “A NOTE ON NATURAL TRANSFORMATION OF MORE GENERALIZED HYPERGEOMETRIC FUNCTION ”, IEJRD - International Multidisciplinary Journal, vol. 6, no. 5, p. 4, Oct. 2021.