On The Generalized Natural Transform
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.
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.
Copyright (c) 2018 Mathematical Journal of Interdisciplinary Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
License and Copyright Policy
Chitkara University Publications for the journal (Math. J. Interdiscip. Sci.) protects author rights e.g., the results, analysis, methodology of Theoretical calculations or experiment. The copyright transfer form with open access policy under the creative common licenses of journal provides all rights specifically to the author (s); except to sell, distribution of the material in any form to any third party. Also, the authors are encouraged to submit the author’s copy of the accepted paper to an appropriate archive e.g. arxive.org and/or in their institution’s repositories, or on their personal website also.
Author(s) should mention reference of the Journal of Chitkara University Publications and DOI number of the publication carefully on the required page of the depository, in all above-mentioned cases. The copyright and license policy of Chitkara University Publications not only protect the author's rights but also protect the integrity and authenticity of the scientific records and takes very seriously about the plagiarism, fraud or ethics disputes.
Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.
View Legal Code of the above mentioned license, https://creativecommons.org/licenses/by/4.0/legalcode
View Licence Deed here https://creativecommons.org/licenses/by/4.0/
|Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in|