<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.</p>
</abstract>

In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Amol University of Special Modern Technologies

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 Public License.

In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov...

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Published Online: Jul 01, 2019

Page range: 289 - 304

Received: Mar 29, 2019

Accepted: May 07, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00026

Keywords
The (3+1)-dimensional space-time fractional mKdV–ZK, the variable separated ODE method, solitons and periodic wave solutions

© 2019 K. S. Al-Ghafri et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

Published Online: Jul 01, 2019

Page range: 289 - 304

Received: Mar 29, 2019

Accepted: May 07, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00026

KeywordsThe (3+1)-dimensional space-time fractional mKdV–ZK, the variable separated ODE method, solitons and periodic wave solutions

© 2019 K. S. Al-Ghafri et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Keywords
The (3+1)-dimensional space-time fractional mKdV–ZK, the variable separated ODE method, solitons and periodic wave solutions