No abstract

This article explores the abundant solitary wave solutions of the conformable coupled Jaulent–Miodek (JM) equations appearing in applied physics. The aforesaid coupled equations belong to the family of shallow-water wave equations. Two recent modified integration schemes are used for the first time to produce a novel solitary wave, trigonometric and other solutions with some free parameters in the conformable derivative sense. In particular, the modified Kudryashov and [Formula: see text]-expansion schemes are used to illustrate the wave propagations through aforesaid solutions of the JM equations. Furthermore, a comparison is made with some recent results and the dynamics of the obtained solutions are displayed for the reader via soft computation. The outcomes reveal that the methods are effective and provide a direct way of finding novel solutions.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

The modified Kudryashov approach along with the conformable derivative is used to find a variety of askew wave solutions, with some free parameters, of the space-time fractional modified KdV equations. We study the wave solutions of the aforesaid mKdV equations that are obliquely propagated to consider the behaviour of physical issues in water waves and other fluids. The graphical depiction of these solutions is given via Mathematica for better understanding. Moreover, apart from the physical implication, these solutions may be helpful for an upgraded understanding of numerical solvers to compare the accuracy of their results and performances of wave dynamics as observed in science and engineering.