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.
Highlights
As of late, nonlinear fractional partial differential equations (FPDEs) are one of the progressing fields of applied mathematics, computational mathematics, and mathematical physics whose thought was first introduced in 1695 [1]
With the assists of potential computer programming software, they have been appointed for researching some appropriate solutions to the nonlinear space-time FPDEs by executing powerful techniques, namely the Legendre collocation method [5], the Adomian decomposition way
Rahhman et al [24] didn't give any fruitful discussion about FPDEs in the sense of conformable derivative with our preferred method
Summary
Nonlinear fractional partial differential equations (FPDEs) are one of the progressing fields of applied mathematics, computational mathematics, and mathematical physics whose thought was first introduced in 1695 [1]. Dimensional space-time fractional AKNS equation [33, 37] with the application of the advanced exp ðÀφ ðξÞÞ-expansion method [23, 24] This method to some fractional and non-fractional PDEs. Rahhman et al [24] didn't give any fruitful discussion about FPDEs in the sense of conformable derivative with our preferred method. Whereupon the obtained exact solutions of their studies [23, 24] are not novel in the sense of conformable time fractional derivative Considering this fact, we firmly intended ourselves to find out the exact solution of the nonlinear conformable space-time fractional (2 þ 1)dimensional AKNS water wave condition with the aid of the advanced exp ðÀφ ðξÞÞ-expansion scheme. With the sense of comformable derivative, there is no pragmatic studies are not found yet about our advanced exp ðÀφ ðξÞÞ-expansion method to investigate the space-time fractional (2 þ 1)-dimensional AKNS water wave equation.
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