Hussain Juya

This study propounds a detailed report on the exact wave solutions of the complex fractional Ginzburg−Landau equation (CFGLE) with quadratic‐cubic law nonlinearity and (4 + 1)‐dimensional fractional Fokas equation (FFE). For this purpose, the aforementioned equations are transformed into nonlinear ordinary differential equations (NLODEs) within the scope of the beta fractional derivative. Then, the new version trial equation method (NVTEM) is applied effectively and featly to derive the rational, exponential, hyperbolic, and Jacobi elliptic−type function solutions. The evaluated solutions are verified by means of the Symbolic Software. Some of the achieved wave solutions are presented in 2D and 3D graphics to advance the essential propagated properties and to present new solitary‐wave structures. The investigated results demonstrate that the proposed analytical method is not only a vigorous mathematical tool but also can be used for various nonlinear models to reveal the exact solutions. This analysis improves the understanding of the wave behaviors in various fields such as optics, plasma physics, fluid mechanics, and engineering.

In this study, the exact solutions of the Biswas-Arshed equation with the beta time derivative, which has an important role and physically means that it represents the pulse propagation in an optical fiber, nuclear, and particle physics, are obtained using the modified exponential function method. Exact solutions consisting of hyperbolic, trigonometric, rational trigonometric, and rational function solutions demonstrate the competence and relevance of the proposed method. In addition, the physical properties of the obtained exact solutions are shown by making graphical representations according to different parameter values. It is seen that the method used is an effective technique, since these solution functions obtained with all these cases have periodic function properties.