Research Article

Conformable variational iteration method

Volume: 5 Number: 1 January 1, 2017
  • Omer Acan *
  • Omer Firat
  • Yildiray Keskin
  • Galip Oturanc
EN

Conformable variational iteration method

Abstract

In this study, we introduce the conformable variational iteration method based on new defined fractional derivative called conformable fractional derivative. This new method is applied two fractional order ordinary differential equations. To see how the solutions of this method, linear homogeneous and non-linear non-homogeneous fractional ordinary differential equations are selected. Obtained results are compared the exact solutions and their graphics are plotted to demonstrate efficiency and accuracy of the method.

Keywords

References

  1. I. Podlubny, Fractional differential equations, Academic Press, 1999.
  2. W.R. Schneider, W. Wyss, Fractional diffusion and wave equations, J. Math. Phys. 30 (1989) 134-144.
  3. H. Beyer, S. Kempfle, Definition of Physically Consistent Damping Laws with Fractional Derivatives, J. Appl. Math. Mech. 75 (1995) 623-635.
  4. F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos, Solitons & Fractals. 7 (1996) 1461-1477.
  5. J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng. 167 (1998) 57-68.
  6. J.H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Int. J. Non. Linear. Mech. 34 (1999) 699-708.
  7. J.H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114 (2000) 115-123.
  8. J.H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B. 20 (2006) 1141-1199.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Omer Acan *
Türkiye

Omer Firat This is me
Türkiye

Yildiray Keskin This is me
Türkiye

Galip Oturanc This is me
Türkiye

Publication Date

January 1, 2017

Submission Date

April 6, 2016

Acceptance Date

April 28, 2016

Published in Issue

Year 2017 Volume: 5 Number: 1

APA
Acan, O., Firat, O., Keskin, Y., & Oturanc, G. (2017). Conformable variational iteration method. New Trends in Mathematical Sciences, 5(1), 172-178. https://izlik.org/JA94RJ43MC
AMA
1.Acan O, Firat O, Keskin Y, Oturanc G. Conformable variational iteration method. New Trends in Mathematical Sciences. 2017;5(1):172-178. https://izlik.org/JA94RJ43MC
Chicago
Acan, Omer, Omer Firat, Yildiray Keskin, and Galip Oturanc. 2017. “Conformable Variational Iteration Method”. New Trends in Mathematical Sciences 5 (1): 172-78. https://izlik.org/JA94RJ43MC.
EndNote
Acan O, Firat O, Keskin Y, Oturanc G (January 1, 2017) Conformable variational iteration method. New Trends in Mathematical Sciences 5 1 172–178.
IEEE
[1]O. Acan, O. Firat, Y. Keskin, and G. Oturanc, “Conformable variational iteration method”, New Trends in Mathematical Sciences, vol. 5, no. 1, pp. 172–178, Jan. 2017, [Online]. Available: https://izlik.org/JA94RJ43MC
ISNAD
Acan, Omer - Firat, Omer - Keskin, Yildiray - Oturanc, Galip. “Conformable Variational Iteration Method”. New Trends in Mathematical Sciences 5/1 (January 1, 2017): 172-178. https://izlik.org/JA94RJ43MC.
JAMA
1.Acan O, Firat O, Keskin Y, Oturanc G. Conformable variational iteration method. New Trends in Mathematical Sciences. 2017;5:172–178.
MLA
Acan, Omer, et al. “Conformable Variational Iteration Method”. New Trends in Mathematical Sciences, vol. 5, no. 1, Jan. 2017, pp. 172-8, https://izlik.org/JA94RJ43MC.
Vancouver
1.Omer Acan, Omer Firat, Yildiray Keskin, Galip Oturanc. Conformable variational iteration method. New Trends in Mathematical Sciences [Internet]. 2017 Jan. 1;5(1):172-8. Available from: https://izlik.org/JA94RJ43MC