Eur. Phys. J. Plus (2019) 134: 322
https://doi.org/10.1140/epjp/i2019-12680-4

Regular Article

Complex surfaces to the fractional (2 + 1)-dimensional Boussinesq dynamical model with the local M-derivative

Harran University, Faculty of Education, Department of Mathematics and Science Education, Sanliurfa, Turkey

^* e-mail: hmbaskonus@gmail.com

Received: 26 February 2019
Accepted: 29 March 2019
Published online: 9 July 2019

Abstract

This manuscript finds new solutions to the fractional (2 + 1)-dimensional Boussinesq dynamical model with the local M -derivative with the help of the modified exponential function method. Many new complex singular and travelling wave solutions are successfully obtained. For deeper investigation of gravity waves propagation on the water surface, 2D and 3D graphs along with contour simulations via several computational programs are used.