Deriving Novel wave solutions to the (۲+۱)-dimensional fractional Paraxial wave dynamical equation with Kerr law using the ({G}'/G^۲) -expansion function technique

The method is used to find traveling wave solutions of nonlinear evolution equations (NLEEs), not "certain types". Specify "to find exact traveling wave solutions to certain types of nonlinear partial differential equations (NLPDEs)". In this case, the Paraxial Wave Dynamical Equation with Kerr law (PWDE) in the sense of the truncated \mathsf{M} -fractional  derivative. This equation is important in the study of wave propagation and optical phenomena. By employing this method, the researchers were able to obtain new, previously unknown exact solutions to this equation. These solutions represent different types of wave solutions, each with their own unique characteristics and properties. The significance of these novel wave solutions lies in their potential applications in physics and engineering. Wave phenomena play a crucial role in various fields, such as optics, photonics, and electromagnetics. The researchers indicate that these specific wave solutions have important practical applications in these domains. Moreover, we provide visual representations of the obtained solutions in the form of ۳D, contour, and ۲D plots. These graphical illustrations serve to demonstrate the feasibility and reliability of our proposed technique, showcasing its ability to capture the essential characteristics and behaviors of the solutions.

کلیدواژه ها:

fractional calculus ، the truncated M-fractional derivative ، Exact solutions ، (G′/G۲)-expansion function method ، Paraxial Wave Dynamical Equation (PWDE)