Research Article

The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method

Volume: 2 Number: 2 December 20, 2019
EN

The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method

Abstract

In this article, authors employed the new sub equation method to attain  new traveling wave solutions of conformable time fractional partial differential equations. Conformable fractional derivative is a well behaved, applicable and understandable definition of arbitrary order derivation. Also this derivative obeys the basic properties that Newtonian concept satisfies. In this study authors obtained the exact solution for KDV equation where the fractional derivative is in conformable sense. New solutions are obtained in terms of the generalized version of the trigonometric functions.

Keywords

References

  1. [1] K. Oldham, J. Spanier, The Fractional Calculus, Theory and Applications of Differentiation and Integration of Arbitrary Order, Academic Press, 1974.
  2. [2] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, 1993.
  3. [3] I. Podlubny, Fractional Differential Equations, Academic Press,1999.
  4. [4] A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, 2006.
  5. [5] A. Kurt, O. Tasbozan, Approximate analytical solution of the time fractional Whitham-Broer-Kaup equation using the homotopy analysis method, Int. J. Pure Appl. Math., 98(4) (2015), 503-510.
  6. [6] O. Tasbozan, A. Esen, N. M. Yagmurlu, Y. Ucar, A numerical solution to fractional diffusion equation for force-free case, Abstr. Appl. Anal., 2013, Hindawi, (2013).
  7. [7] C. Celik, M. Duman, Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative, J. of Comput. Phys., 231(4) (2012), 1743-1750.
  8. [8] Y. Cenesiz, A. Kurt, New fractional complex transform for conformable fractional partial differential equations, J. Appl. Math. Stat. Inf., 12(2) (2016), 41-47.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

December 20, 2019

Submission Date

May 10, 2019

Acceptance Date

October 26, 2019

Published in Issue

Year 2019 Volume: 2 Number: 2

APA
Kurt, A., Tasbozan, O., & Durur, H. (2019). The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method. Fundamental Journal of Mathematics and Applications, 2(2), 173-179. https://doi.org/10.33401/fujma.562819
AMA
1.Kurt A, Tasbozan O, Durur H. The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method. Fundam. J. Math. Appl. 2019;2(2):173-179. doi:10.33401/fujma.562819
Chicago
Kurt, Ali, Orkun Tasbozan, and Hulya Durur. 2019. “The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method”. Fundamental Journal of Mathematics and Applications 2 (2): 173-79. https://doi.org/10.33401/fujma.562819.
EndNote
Kurt A, Tasbozan O, Durur H (December 1, 2019) The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method. Fundamental Journal of Mathematics and Applications 2 2 173–179.
IEEE
[1]A. Kurt, O. Tasbozan, and H. Durur, “The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method”, Fundam. J. Math. Appl., vol. 2, no. 2, pp. 173–179, Dec. 2019, doi: 10.33401/fujma.562819.
ISNAD
Kurt, Ali - Tasbozan, Orkun - Durur, Hulya. “The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method”. Fundamental Journal of Mathematics and Applications 2/2 (December 1, 2019): 173-179. https://doi.org/10.33401/fujma.562819.
JAMA
1.Kurt A, Tasbozan O, Durur H. The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method. Fundam. J. Math. Appl. 2019;2:173–179.
MLA
Kurt, Ali, et al. “The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method”. Fundamental Journal of Mathematics and Applications, vol. 2, no. 2, Dec. 2019, pp. 173-9, doi:10.33401/fujma.562819.
Vancouver
1.Ali Kurt, Orkun Tasbozan, Hulya Durur. The Exact Solutions of Conformable Fractional Partial Differential Equations Using New Sub Equation Method. Fundam. J. Math. Appl. 2019 Dec. 1;2(2):173-9. doi:10.33401/fujma.562819

Cited By

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