<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The main purpose of this article is to obtain the new solutions of fractional bad and good modified Boussinesq equations with the aid of auxiliary equation method, which can be considered as a model of shallow water waves. By using the conformable wave transform and chain rule, nonlinear fractional partial differential equations are converted into nonlinear ordinary differential equations. This is an important impact because both Caputo definition and Riemann–Liouville definition do not satisfy the chain rule. By using conformable fractional derivatives, reliable solutions can be achieved for conformable fractional partial differential equations.</p></abstract>

The main purpose of this article is to obtain the new solutions of fractional bad and good modified Boussinesq equations with the aid of auxiliary equation method, which can be considered as a model of shallow water waves. By using the conformable wave transform and chain rule, nonlinear fractional partial differential equations are converted into nonlinear ordinary differential equations. This is an important impact because both Caputo definition and Riemann–Liouville definition do not satisfy the chain rule. By using conformable fractional derivatives, reliable solutions can be achieved for conformable fractional partial differential equations.

New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations

Department of Computer Engineering, Faculty of Engineering

Department of Mathematics, Faculty of Science and Art

Applied Mathematics and Nonlinear Sciences

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

The main purpose of this article is to obtain the new solutions of fractional bad and good modified Boussinesq equations with the aid of auxiliary equation...

New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations

Published Online: Apr 10, 2020

Page range: 447 - 454

Received: May 14, 2019

Accepted: Jun 22, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00042

Keywords
bad and good modified Boussinesq equations, conformable fractional derivative, auxiliary equation method

© 2020 Hülya Durur et al., published by Sciendo

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

New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations

Published Online: Apr 10, 2020

Page range: 447 - 454

Received: May 14, 2019

Accepted: Jun 22, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00042

Keywordsbad and good modified Boussinesq equations, conformable fractional derivative, auxiliary equation method

© 2020 Hülya Durur et al., published by Sciendo

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

Keywords
bad and good modified Boussinesq equations, conformable fractional derivative, auxiliary equation method