Analytical solutions of conformable time, space, and time-space fractional KdV equations

Authors

HASİBE HALE KARAYER
AHMET DOĞAN DEMİRHAN
FEVZİ BÜYÜKKILIÇ

DOI

10.3906/fiz-1711-17

Abstract

In this study, we consider the Korteweg-de Vries (KdV) equation for solitary waves in the domain of conformable fractional calculus. By means of this fractional theory, we obtain exact solutions for time, space, and time-space fractional KdV equations and demonstrate our results graphically according to the fractional order of the related equations. Furthermore, we report that the fractional order in the solution of the time fractional KdV equation is associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of time fractional KdV and Burgers-KdV equations.

Keywords

KdV equation, conformable fractional KdV equation, conformable fractional calculus

First Page

254

Last Page

264

Recommended Citation

KARAYER, HASİBE HALE; DEMİRHAN, AHMET DOĞAN; and BÜYÜKKILIÇ, FEVZİ (2018) "Analytical solutions of conformable time, space, and time-space fractional KdV equations," Turkish Journal of Physics: Vol. 42: No. 3, Article 3. https://doi.org/10.3906/fiz-1711-17
Available at: https://journals.tubitak.gov.tr/physics/vol42/iss3/3