Dynamical analysis of long-wave phenomena for the nonlinear conformable space-time fractional (2+1)-dimensional AKNS equation in water wave mechanics

Nur Hasan Mahmud Shahen; Foyjonnesa; Md Habibul Bashar; Md Shuzon Ali; Abdulla-Al- Mamun

doi:10.1016/j.heliyon.2020.e05276

Dynamical analysis of long-wave phenomena for the nonlinear conformable space-time fractional (2+1)-dimensional AKNS equation in water wave mechanics

Heliyon. 2020 Oct 23;6(10):e05276. doi: 10.1016/j.heliyon.2020.e05276. eCollection 2020 Oct.

Authors

Nur Hasan Mahmud Shahen^{1

2}, Foyjonnesa^{1

3}, Md Habibul Bashar¹, Md Shuzon Ali^{3

2}, Abdulla-Al- Mamun⁴

Affiliations

¹ European University of Bangladesh, Dhaka 1216, Bangladesh.
² Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalgonj 8100, Bangladesh.
³ University of Rajshahi, Rajshai 6205, Bangladesh.
⁴ Islamic University, Kushtia 7003, Bangladesh.

Abstract

The main intension of this paper is to extract new and further general analytical wave solutions to the (2 + 1)-dimensional fractional Ablowitz-Kaup-Newell-Segur (AKNS) equation in the sense of conformable derivative by implementing the advanced $exp (- ϕ (ξ))$ -expansion method. This method is a particular invention of the generalized $exp (- ϕ (ξ))$ -expansion method. By the virtue of the advanced $exp (- ϕ (ξ))$ -expansion method, a series of kink, singular kink, soliton, combined soliton, and periodic wave solutions are constructed to our preferred space time-fractional (2 + 1)- dimensional AKNS equation. An extensive class of new exact traveling wave solutions are transpired in terms of, hyperbolic, trigonometric, and rational functions. To express the underlying propagated features, some attained solutions are exhibited by making their three-dimensional (3D), two-dimensional (2D) combined, and 2D line plot with the help of computational packages MATLAB. All plots are given to show the proper wave features through the founded solutions to the studied equation with particular preferring of the selected parameters. Moreover, it may conclude that the attained solutions and their physical features might be helpful to comprehend the water wave propagation in water wave mechanics.

Keywords: Applied mathematics; Conformable derivative; Nonlinear physics; Space-time fractional (2+1)-dimensional AKNS equation; The advanced exp ( - ϕ ( ξ ) ) -expansion method.