On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method

Sayed K. Elagan; Mohamed S. Mohamed; Khaled A. Gepreel; Rabha W. Ibrahim; Afaf Elesimy

doi:doi:10.11648/j.sjams.20140206.12

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On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method

Sayed K. Elagan, Mohamed S. Mohamed, Khaled A. Gepreel, Rabha W. Ibrahim, Afaf Elesimy

Published in Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 6)

Received: 28 November 2014 Accepted: 6 December 2014 Published: 17 December 2014

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Abstract

We provide a new solution of diffusion fractional differential equation using fractal index and fractional sub-equation method. Also we shall impose a new solution for fraction Birnolli equation of arbitrary order using the fractal index method. As a result many exact solutions are obtained. It is shown that our considered method provides a very effective tool for solving fractional differentional equations.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 6)
DOI	10.11648/j.sjams.20140206.12
Page(s)	112-115
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

Fractional Sub-Equation Method, Fractal Index Method

References

[1]	I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
[2]	A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
[3]	J. Sabatier, O. P. Agrawal, and J. A. Machado, Advance in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.
[4]	V. Lakshmikantham, S. Leela, J. Vasundhara, Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge 2009.
[5]	D. Baleanu, B. Guvenc and J. A. Tenreiro, New Trends in Nanotechnology and Fractional Calculus Applications, Springer, New York, NY, USA, 2010.
[6]	P. R. Gordoa, A. Pickering, Z. N. Zhu, Bucklund transformations for a matrix second Painlev equation, Physics Letters A, 374 (34) (2010) 3422-3424.
[7]	R. Molliq, B. Batiha, Approximate analytic solutions of fractional Zakharov-Kuznetsov equations by fractional complex transform, International Journal of Engineering and Technology, 1 (1) (2012) 1-13.
[8]	R.W. Ibrahim, Complex transforms for systems of fractional differential equations, Abstract and Applied Analysis Volume 2012, Article ID 814759, 15 pages.
[9]	S. Sivasubramanian, M. Darus, R. W. Ibrahim, On the starlikeness of certain class of analytic functions, Mathematical and Computer Modelling, vol. 54, no. -2(2011) pp. 112118.
[10]	R. W. Ibrahim, An application of Lauricella hypergeometric functions to the generalized heat equations, Malaya Journal of Matematik, 1(2014) 43-48.
[11]	Zheng-Biao Li and Ji-Huan He. "Application of the ractional Complex Transform to Fractional Differential Equations"Nonlinear Science Letters A- Mathematics, Physics and Mechanics 2.3 (2011): 121-126.
[12]	Ji-Huan He a, S.K. Elagan and Z.B. Li c, Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus Physics Letters A 376 (2012) 257–259.
[13]	RabhaW. Ibrahima, and S. K. Elagan, On solutions for classes of fractional differential equations, Malaya J. Mat. 2(4) (2014) 411–418.
[14]	J. R. Macdonald, L. R. Evangelista, E. K. Lenzi, and G. Barbero, J. Phys. Chem. C, 115(2011) 7648-7655.
[15]	P. A. Santoro, J. L. de Paula, E. K. Lenzi, L. R. Evangelista, J. Chem. Phys. 135(114704)(2011) 1-5.
[16]	J.T. Machado, V. Kiryakova, F. Mainardi, Commun. Nonlinear Sci. 16(2011) 1140- 1153.
[17]	R. W. Ibrahim, On holomorphic solution for space- and time-fractional telegraph equations in complex domain, Journal of Function Spaces and Applications 2012, Article ID 703681, 10 pages.
[18]	R.W. Ibrahim, Numerical solution for complex systems of fractional order, Journal of Applied Mathematics 2012, Article ID 678174, 11 pages.
[19]	K. Diethelm, The Analysis of Fractional Differential Equations, Springer-Verlag Berlin Heidelberg, 2010.
[20]	S. Zhang, H.Q. Zhang, Fractional sub-equation method and its applications to nonlinear fractional PDEs, Phys. Lett. A, 375 (2011) 1069-1073.
[21]	A. N. Kochubei, The Cauchy problem for evolution equations of fractional order, Differential Equations 25 (1989) 967-974.
[22]	A. N. Kochubei, Diffusion of fractional order, Differential Equations 26 (1990) 485-492.
[23]	R. Metzler, J. Klafter, The random walks guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 (2000) 1-77.
[24]	G. Zaslavsky, Fractional kinetic equation for Hamiltonian chaos. Chaotic advection, tracer dynamics and turbulent dispersion. Phys. D 76 (1994) 110-122.
[25]	F. Mainardi, G. Pagnini and R. Gorenflo; Some aspects of fractional diffusion equations of single and distributed order, App. Math. Compu., 187( 1) (2007) 295-305.
[26]	Khaled A. Gepreel and Mohamed S. Mohamed, Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation, Chinese physics B, Vol. 22, Issue. 1, 2013, 010201-6.
[27]	Hossam A. Ghany and Mohamed S. Mohamed, White noise functional solutions for the wick-type stochastic fractional Kdv-Burgers-Kuramoto Equations, Journal of the Chinese Journal of Physics. Vol. 50, Issue. 4, 2012, pp. 619-627.

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APA Style

Sayed K. Elagan, Mohamed S. Mohamed, Khaled A. Gepreel, Rabha W. Ibrahim, Afaf Elesimy. (2014). On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method. Science Journal of Applied Mathematics and Statistics, 2(6), 112-115. https://doi.org/10.11648/j.sjams.20140206.12

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ACS Style

Sayed K. Elagan; Mohamed S. Mohamed; Khaled A. Gepreel; Rabha W. Ibrahim; Afaf Elesimy. On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method. Sci. J. Appl. Math. Stat. 2014, 2(6), 112-115. doi: 10.11648/j.sjams.20140206.12

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AMA Style

Sayed K. Elagan, Mohamed S. Mohamed, Khaled A. Gepreel, Rabha W. Ibrahim, Afaf Elesimy. On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method. Sci J Appl Math Stat. 2014;2(6):112-115. doi: 10.11648/j.sjams.20140206.12

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@article{10.11648/j.sjams.20140206.12,
  author = {Sayed K. Elagan and Mohamed S. Mohamed and Khaled A. Gepreel and Rabha W. Ibrahim and Afaf Elesimy},
  title = {On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {2},
  number = {6},
  pages = {112-115},
  doi = {10.11648/j.sjams.20140206.12},
  url = {https://doi.org/10.11648/j.sjams.20140206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140206.12},
  abstract = {We provide a new solution of diffusion fractional differential equation using fractal index and fractional sub-equation method. Also we shall impose a new solution for fraction Birnolli equation of arbitrary order using the fractal index method. As a result many exact solutions are obtained. It is shown that our considered method provides a very effective tool for solving fractional differentional equations.},
 year = {2014}
}

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TY  - JOUR
T1  - On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method
AU  - Sayed K. Elagan
AU  - Mohamed S. Mohamed
AU  - Khaled A. Gepreel
AU  - Rabha W. Ibrahim
AU  - Afaf Elesimy
Y1  - 2014/12/17
PY  - 2014
N1  - https://doi.org/10.11648/j.sjams.20140206.12
DO  - 10.11648/j.sjams.20140206.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 112
EP  - 115
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20140206.12
AB  - We provide a new solution of diffusion fractional differential equation using fractal index and fractional sub-equation method. Also we shall impose a new solution for fraction Birnolli equation of arbitrary order using the fractal index method. As a result many exact solutions are obtained. It is shown that our considered method provides a very effective tool for solving fractional differentional equations.
VL  - 2
IS  - 6
ER  -

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Author Information

Sayed K. Elagan

Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia
Mohamed S. Mohamed

Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia
Khaled A. Gepreel

Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia
Rabha W. Ibrahim

Institute of Mathematical Sciences, University Malaya, 50603, Kuala Lumpur, Malaysia
Afaf Elesimy

Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia

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Plain Text BibTeX RIS

APA Style

Sayed K. Elagan, Mohamed S. Mohamed, Khaled A. Gepreel, Rabha W. Ibrahim, Afaf Elesimy. (2014). On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method. Science Journal of Applied Mathematics and Statistics, 2(6), 112-115. https://doi.org/10.11648/j.sjams.20140206.12

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ACS Style

Sayed K. Elagan; Mohamed S. Mohamed; Khaled A. Gepreel; Rabha W. Ibrahim; Afaf Elesimy. On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method. Sci. J. Appl. Math. Stat. 2014, 2(6), 112-115. doi: 10.11648/j.sjams.20140206.12

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AMA Style

Sayed K. Elagan, Mohamed S. Mohamed, Khaled A. Gepreel, Rabha W. Ibrahim, Afaf Elesimy. On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method. Sci J Appl Math Stat. 2014;2(6):112-115. doi: 10.11648/j.sjams.20140206.12

Copy | Download

@article{10.11648/j.sjams.20140206.12,
  author = {Sayed K. Elagan and Mohamed S. Mohamed and Khaled A. Gepreel and Rabha W. Ibrahim and Afaf Elesimy},
  title = {On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {2},
  number = {6},
  pages = {112-115},
  doi = {10.11648/j.sjams.20140206.12},
  url = {https://doi.org/10.11648/j.sjams.20140206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140206.12},
  abstract = {We provide a new solution of diffusion fractional differential equation using fractal index and fractional sub-equation method. Also we shall impose a new solution for fraction Birnolli equation of arbitrary order using the fractal index method. As a result many exact solutions are obtained. It is shown that our considered method provides a very effective tool for solving fractional differentional equations.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - On Solving Some Classes of Nonlinear Fractional Differentional Equations Using Fractal Index Method
AU  - Sayed K. Elagan
AU  - Mohamed S. Mohamed
AU  - Khaled A. Gepreel
AU  - Rabha W. Ibrahim
AU  - Afaf Elesimy
Y1  - 2014/12/17
PY  - 2014
N1  - https://doi.org/10.11648/j.sjams.20140206.12
DO  - 10.11648/j.sjams.20140206.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 112
EP  - 115
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20140206.12
AB  - We provide a new solution of diffusion fractional differential equation using fractal index and fractional sub-equation method. Also we shall impose a new solution for fraction Birnolli equation of arbitrary order using the fractal index method. As a result many exact solutions are obtained. It is shown that our considered method provides a very effective tool for solving fractional differentional equations.
VL  - 2
IS  - 6
ER  -

Copy | Download