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2 Journal of Applied Mathematics and Computational Mechanics

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Cubic nonlinear fractional Schrödinger equation with conformable derivative and its new travelling wave solutions

Gündoğdu Hami, Gözükızıl Ömer Faruk

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 2

29--41

In the present paper, the fractional-order cubic nonlinear Schrödinger equation is considered. The Schrödinger equation with time and space fractional derivative is studied at the same time. Different types of travelling wave solutions including the kink solution, soliton solution, periodic solution, and singular solution for the mentioned equation are obtained by using the Jacobi elliptic functions expansion method. It is shown that the solutions turn into the exact solutions when the fractional orders go to 1. This method can be relied on gaining the solutions to time or space fractional order partial differential equations as well as ordinary ones. Throughout this work, the fractional derivative is given in a conformable sense.

On different kinds of solutions to simplified modified form of a Camassa-Holm equation

Gündoğdu Hami, Gözükızıl Ömer Faruk

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 2

31--40

In this research, our purpose is to investigate some types of solutions to a simplified modified form of the Camassa-Holm equation. The Jacobi elliptic function expansion method is applied to this equation. Then, a lot of travelling wave solutions are obtained. The derived solutions are in the form of Jacobi elliptic functions, hyperbolic functions, and trigonometric functions. Graphics of solutions are drawn in order to determine the types of the solutions. Furthermore, different kinds of solutions such as the singular kink wave solution, the kink wave solution, and the periodic solution are achieved.