On The Generalized Natural Transform

  • A.D. Chindhe Department of Mathematics, Balbhim College, Beed, 431 122, Maharashtra, India
  • S B Kiwne Department of Mathematics, Deogiri College, Aurangabad, 431 005, Maharashtra, India
Keywords: Natural Transform, Distribution theory, Convolution theorem

Abstract

In this paper, we introduce the Natural transform in the generalized sense with the help of distribution theory. Inversion, Uniqueness theorems and some properties of generalized in¬tegral transform are proved.

Downloads

Download data is not yet available.

References

Khan Z. H., Khan W.A. (2008). N-transform properties and applications. NUST Journal of Engineering Sciences.1(1), 127–133.

Silambarasan R., Belgacem F. B. M. (2011). Applications of the Natural transform to Maxwell’s Equations. PIERS Suzhou, China. 899–902.

Belgacem F. B. M., Silambarasan R. (2012). Theory of the Natural transform. Mathematics in Engineering Science and Aerospace(MESA)journal. 3(1), 99–124.

Silambarasan R., Belgacem F. B. M. (2012). Advances in the Natural transform. 9th International Conference on Mathematical Problems in Engineering. Aerospace and Sciences AIP Conference Proceeding. 1493,106–110.

Loonker D., Banerji P.K. (2013). Natural transform for distribution and Boehmian spaces. Mathematics in Engineering Science and Aerospace. 4(1), 69–76.

Loonker D., Banerji P. K. (2013). Application of Natural transform to differential equations Journal Indian Academy of Mathematics. 35(1), 151–158.

Chindhe A.D., Kiwne S.B. (2016). Application of Combine Natural Transform and Adomian Decomposition Method in Volterra Integro-Differential Equations. Mathematical Journal of Interdisciplinary Sciences. 5(1), 1–14.

Chindhe A. D., Kiwne S. B. (2017). Natural Transform and Special Functions. Journal of New Theory. 15, 39–47.

Kamal S., Muhammad J., Nigar A. (2015). Extraction of Laplace, Sumudu, Fourier and Mellin Transform from the Natural Transform, J. Appl. Environ. Biol. Sci., 5(9), 108–115.

Loonker D., Banerji P.K. (2013). Natural transform for distribution and Boehmian spaces, Mathematics in Engineering, Science and Aerospace (MESA), 4, No. 1, 69–76.

Al-Omari S.K.Q. (2014). On The Generalized Sumudo Transform., Journal of Applied Functional Analysis, Jan-Apr, 9 Issue 1/2, 42–53.

Loonker D. and Banerji P.K. (2011). On the solution of distributional Abel integral equation by distributional Sumudu transform, Internat. J. Math. Math. Sci. 2011, 1-8, Article ID 480528.

Loonker D. and Banerji P. K. (2012). Fractional Integrals and Derivatives for Sumudu transform on distribution spaces, Appl. Appl. Math. Internat. J. 7(1), 188–200.

Loonker D., Banerji P. K. and Lokenath D. (2010). Hartley Transform for Integrable Boehmians, Int. Trans. Spl. Funct. 21(6), 459–464.

Shah K., Muhammad J. and Nigar A. (2015). Extraction of Laplace, Sumudu, Fourier and Mellin Transform from the Natural Transform, J. Appl. Environ. Biol. Sci., 5(9), 108–115.

Pathak R. S. (1997). Integral Transforms of Generalized Functions and their Applications. Gordon and Breach Science Publishers, Australia, Canada, India, Japan.

Schwartz L. (1950,1951). Th’eorie des Distributions, 2 Vols., Hermann, Paris.

Zemanian A. H. (1965, 1987). Distribution Theory and Transform Analysis : An Introduction to Generalized Functions, with Applications, Mc-Graw Hill, New York, Republished by Dover Publication, Inc., New York.

Zemanian A.H. (1968, 1987). Generalized Integral Transformations, Interscience Publishers, New York, Republished by Dover Publications, Inc., New York.

Published
2018-09-06
How to Cite
A.D. Chindhe, & S B Kiwne. (2018). On The Generalized Natural Transform. Mathematical Journal of Interdisciplinary Sciences, 7(1), 9-13. Retrieved from https://mjis.chitkara.edu.in/index.php/mjis/article/view/46
Section
Articles