Pure and Applied Mathematics Journal

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A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform

Received: 07 August 2016    Accepted: 20 August 2016    Published: 07 September 2016
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Abstract

In this paper we discuss some relationship between Laplace transform and the new two transform called ELzaki transform and Aboodh transform. We solve first and second order ordinary differential equations using both transforms, and show that ELzaki transform and Aboodh transform are closely connected with the Laplace transform.

DOI 10.11648/j.pamj.20160505.11
Published in Pure and Applied Mathematics Journal (Volume 5, Issue 5, October 2016)
Page(s) 145-150
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Laplace Transform, Elzaki Transform, Aboodh Transform, Differential Equation

References
[1] Tarig M. Elzaki, (2011), The New Integral Transform “Elzaki Transform” Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 57-64.
[2] Tarig M. Elzaki&Salih M. Elzaki, (2011), Application of New Transform “Elzaki Transform” to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 65-70.
[3] Tarig M. Elzaki&Salih M. Elzaki, (2011), On the Connections between Laplace and Elzaki transforms, Advances in Theoretical and Applied Mathematics, ISSN 0973-4554 Volume 6, Number 1, pp. 1-11.
[4] Tarig M. Elzaki&Salih M. Elzaki, (2011), On the Elzaki Transform and Ordinary Differential Equation With Variable Coefficients, Advances in Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6, Number 1, pp. 13-18.
[5] D. D. Ganji, The applications of He’s homotopy perturbation method to nonlinear equation arising in heat transfer, Physics Letters A, 335 (2006): 337–341.
[6] A. Kilicman and H. E. Gadain. (2009), An application of double Laplace transform and Sumudu transform, Lobachevskii J. Math. 30 (3), pp. 214-223. http://dx.doi.org/10.1134/s1995080209030044
[7] J. Zhang, (2007), A Sumudu based algorithm m for solving differential equations, Comp. Sci. J. Moldova 15 (3), pp - 303-313.
[8] Hassan Eltayeb and AdemKilicman, (2010), A Note on the Sumudu Transforms and differential Equations, Applied Mathematical Sciences, VOL, 4, no. 22, 1089-1098.
[9] Kilicman A. & H. ELtayeb. (2010), A note on Integral transform and Partial Differential Equation, Applied Mathematical Sciences, 4 (3), PP. 109-118.
[10] Hassan ELtayeh and AdemKilicman, (2010), on Some Applications of a new Integral Transform, Int. Journal of Math. Analysis, Vol, 4, no. 3, 123-132.
[11] K. S. Aboodh, The New Integral Transform “Aboodh Transform” Global Journal of pure and Applied Mathematics, 9 (1), 35-43 (2013).
[12] K. S. Aboodh, Application of New Transform “Aboodh transform” to Partial Differential Equations, Global Journal of pure and Applied Math, 10 (2), 249-254 (2014).
Author Information
  • Mathematics Department Faculty of Sciences and Arts-Almikwah, Albaha University, Albaha, Saudi Arabia;Mathematics Department Faculty of Education, Alzaeim Alazhari University, Khartoum, Sudan

  • Mathematics Department Faculty of Sciences and Arts-Almikwah, Albaha University, Albaha, Saudi Arabia;Mathematics Department Faculty of Sciences, Omderman Islamic University, Khartoum, Sudan

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  • APA Style

    Abdelbagy A. Alshikh, Mohand M. Abdelrahim Mahgob. (2016). A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform. Pure and Applied Mathematics Journal, 5(5), 145-150. https://doi.org/10.11648/j.pamj.20160505.11

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    ACS Style

    Abdelbagy A. Alshikh; Mohand M. Abdelrahim Mahgob. A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform. Pure Appl. Math. J. 2016, 5(5), 145-150. doi: 10.11648/j.pamj.20160505.11

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    AMA Style

    Abdelbagy A. Alshikh, Mohand M. Abdelrahim Mahgob. A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform. Pure Appl Math J. 2016;5(5):145-150. doi: 10.11648/j.pamj.20160505.11

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  • @article{10.11648/j.pamj.20160505.11,
      author = {Abdelbagy A. Alshikh and Mohand M. Abdelrahim Mahgob},
      title = {A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform},
      journal = {Pure and Applied Mathematics Journal},
      volume = {5},
      number = {5},
      pages = {145-150},
      doi = {10.11648/j.pamj.20160505.11},
      url = {https://doi.org/10.11648/j.pamj.20160505.11},
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      abstract = {In this paper we discuss some relationship between Laplace transform and the new two transform called ELzaki transform and Aboodh transform. We solve first and second order ordinary differential equations using both transforms, and show that ELzaki transform and Aboodh transform are closely connected with the Laplace transform.},
     year = {2016}
    }
    

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