An Analytical Treatment to Fractional Gas Dynamics Equation

Mohamed S. Al-luhaibi; Nahed A. Saker

doi:doi:10.11648/j.acm.20140306.16

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An Analytical Treatment to Fractional Gas Dynamics Equation

Mohamed S. Al-luhaibi, Nahed A. Saker

Published in Applied and Computational Mathematics (Volume 3, Issue 6)

Received: 24 October 2014 Accepted: 9 December 2014 Published: 29 December 2014

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Abstract

In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations.

Published in	Applied and Computational Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.acm.20140306.16
Page(s)	323-329
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), 2014. Published by Science Publishing Group

Keywords

Sumudu Transform Method, Adomian Decomposion Method, New Iterative Method,Fractional Gas Dynamics Equation

References

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Mohamed S. Al-luhaibi, Nahed A. Saker. (2014). An Analytical Treatment to Fractional Gas Dynamics Equation. Applied and Computational Mathematics, 3(6), 323-329. https://doi.org/10.11648/j.acm.20140306.16

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ACS Style

Mohamed S. Al-luhaibi; Nahed A. Saker. An Analytical Treatment to Fractional Gas Dynamics Equation. Appl. Comput. Math. 2014, 3(6), 323-329. doi: 10.11648/j.acm.20140306.16

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AMA Style

Mohamed S. Al-luhaibi, Nahed A. Saker. An Analytical Treatment to Fractional Gas Dynamics Equation. Appl Comput Math. 2014;3(6):323-329. doi: 10.11648/j.acm.20140306.16

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@article{10.11648/j.acm.20140306.16,
  author = {Mohamed S. Al-luhaibi and Nahed A. Saker},
  title = {An Analytical Treatment to Fractional Gas Dynamics Equation},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {323-329},
  doi = {10.11648/j.acm.20140306.16},
  url = {https://doi.org/10.11648/j.acm.20140306.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.16},
  abstract = {In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and   Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations.},
 year = {2014}
}

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TY  - JOUR
T1  - An Analytical Treatment to Fractional Gas Dynamics Equation
AU  - Mohamed S. Al-luhaibi
AU  - Nahed A. Saker
Y1  - 2014/12/29
PY  - 2014
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DO  - 10.11648/j.acm.20140306.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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PB  - Science Publishing Group
SN  - 2328-5613
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AB  - In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and   Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations.
VL  - 3
IS  - 6
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Author Information

Mohamed S. Al-luhaibi

Department of Mathematics, Faculty of Science, Kirkuk University, Iraq
Nahed A. Saker

Department of Mathematics, Faculty of Science, Menoufia University, Egypt

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Mohamed S. Al-luhaibi, Nahed A. Saker. (2014). An Analytical Treatment to Fractional Gas Dynamics Equation. Applied and Computational Mathematics, 3(6), 323-329. https://doi.org/10.11648/j.acm.20140306.16

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ACS Style

Mohamed S. Al-luhaibi; Nahed A. Saker. An Analytical Treatment to Fractional Gas Dynamics Equation. Appl. Comput. Math. 2014, 3(6), 323-329. doi: 10.11648/j.acm.20140306.16

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AMA Style

Mohamed S. Al-luhaibi, Nahed A. Saker. An Analytical Treatment to Fractional Gas Dynamics Equation. Appl Comput Math. 2014;3(6):323-329. doi: 10.11648/j.acm.20140306.16

Copy | Download

@article{10.11648/j.acm.20140306.16,
  author = {Mohamed S. Al-luhaibi and Nahed A. Saker},
  title = {An Analytical Treatment to Fractional Gas Dynamics Equation},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {323-329},
  doi = {10.11648/j.acm.20140306.16},
  url = {https://doi.org/10.11648/j.acm.20140306.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.16},
  abstract = {In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and   Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - An Analytical Treatment to Fractional Gas Dynamics Equation
AU  - Mohamed S. Al-luhaibi
AU  - Nahed A. Saker
Y1  - 2014/12/29
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140306.16
DO  - 10.11648/j.acm.20140306.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 323
EP  - 329
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140306.16
AB  - In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and   Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations.
VL  - 3
IS  - 6
ER  -

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