Research Article

Elzaki transform combined with variational iteration method for partial differential equations of fractional order

Volume: 1 Number: 1 June 30, 2018
EN

Elzaki transform combined with variational iteration method for partial differential equations of fractional order

Abstract

The idea, which will be communicated through this paper is to make a change to the proposed method by Tarig M. Elzaki [6] and we extend it to solve nonlinear partial differential equations with time-fractional derivative. This document also includes illustrative examples show us how to apply this method, we also show the interest of combining these two methods is the speed of the calculates the terms, and not calculating the Lagrange multipliers.

Keywords

References

  1. [1] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  2. [2] A. Neamaty, B. Agheli and R. Darzi, New Integral Transform for Solving Nonlinear Partial Differential Equations of fractional order, Theor. Appr. Appl. 10(1), (2014), 69-86., [3] A. S. Abedl-Rady, S. Z. Rida, A. A. M. Arafa and H. R Abedl-Rahim, Variational Iteration Sumudu Transform Method for Solving Fractional Nonlinear Gas Dynamics Equation, Int. J. Res. Stu. Sci. Eng. Tech. 1 (2014), 82-90.
  3. [4] A. S. Arife and A. Yildirim, New Modified Variational Iteration Transform Method (MVITM) for solving eighth-order Boundary value problems in one Step, W. Appl. Sci. J. 13 (2011), 2186 -2190.
  4. [5] D. Kumar, J. Singh and S. Rathore, Sumudu Decomposition Method for Nonlinear Equations, Int. Math. For. 7 (2012), 515-521.
  5. [6] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
  6. [7] J. H. He and X. H. Wu, Variational iteration method: new development and applications, Comput. Math. Appl. 54(7/8), (2007), 881-894.
  7. [8] J. H. He, A variational iteration approach to nonlinear problems and its applications, Mech. Appl. 20(1), (1998), 30-31.
  8. [9] J. H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114(2/3), (2000), 115-123.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

June 30, 2018

Submission Date

April 17, 2018

Acceptance Date

June 10, 2018

Published in Issue

Year 2018 Volume: 1 Number: 1

APA
Ziane, D., Elzaki, T. M., & Hamdi Cherif, M. (2018). Elzaki transform combined with variational iteration method for partial differential equations of fractional order. Fundamental Journal of Mathematics and Applications, 1(1), 102-108. https://doi.org/10.33401/fujma.415892
AMA
1.Ziane D, Elzaki TM, Hamdi Cherif M. Elzaki transform combined with variational iteration method for partial differential equations of fractional order. Fundam. J. Math. Appl. 2018;1(1):102-108. doi:10.33401/fujma.415892
Chicago
Ziane, Djelloul, Tarig M Elzaki, and Mountassir Hamdi Cherif. 2018. “Elzaki Transform Combined With Variational Iteration Method for Partial Differential Equations of Fractional Order”. Fundamental Journal of Mathematics and Applications 1 (1): 102-8. https://doi.org/10.33401/fujma.415892.
EndNote
Ziane D, Elzaki TM, Hamdi Cherif M (June 1, 2018) Elzaki transform combined with variational iteration method for partial differential equations of fractional order. Fundamental Journal of Mathematics and Applications 1 1 102–108.
IEEE
[1]D. Ziane, T. M. Elzaki, and M. Hamdi Cherif, “Elzaki transform combined with variational iteration method for partial differential equations of fractional order”, Fundam. J. Math. Appl., vol. 1, no. 1, pp. 102–108, June 2018, doi: 10.33401/fujma.415892.
ISNAD
Ziane, Djelloul - Elzaki, Tarig M - Hamdi Cherif, Mountassir. “Elzaki Transform Combined With Variational Iteration Method for Partial Differential Equations of Fractional Order”. Fundamental Journal of Mathematics and Applications 1/1 (June 1, 2018): 102-108. https://doi.org/10.33401/fujma.415892.
JAMA
1.Ziane D, Elzaki TM, Hamdi Cherif M. Elzaki transform combined with variational iteration method for partial differential equations of fractional order. Fundam. J. Math. Appl. 2018;1:102–108.
MLA
Ziane, Djelloul, et al. “Elzaki Transform Combined With Variational Iteration Method for Partial Differential Equations of Fractional Order”. Fundamental Journal of Mathematics and Applications, vol. 1, no. 1, June 2018, pp. 102-8, doi:10.33401/fujma.415892.
Vancouver
1.Djelloul Ziane, Tarig M Elzaki, Mountassir Hamdi Cherif. Elzaki transform combined with variational iteration method for partial differential equations of fractional order. Fundam. J. Math. Appl. 2018 Jun. 1;1(1):102-8. doi:10.33401/fujma.415892

Cited By

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