Construction of the Closed Form Wave Solutions for TFSMCH and (1 + 1) Dimensional TFDMBBM Equations via the EMSE Technique - Md. Asaduzzaman; Farhana Jesmin (Fractal and Fractional)
The purpose of this study is to investigate a series of novel exact closed form traveling wave solutions for the TFSMCH equation and (1 + 1) dimensional TFDMBBM equation using the EMSE technique. The considered FONLEEs are used to delineate the characteristic of diffusion in the creation of shapes in liquid beads arising in plasma physics and fluid flow and to estimate the external long waves in nonlinear dispersive media. These equations are also used to characterize various types of waves, such as hydromagnetic waves, acoustic waves, and acoustic gravity waves. Here, we utilize the Caputo-type fractional order derivative to fractionalize the considered FONLEEs. Some trigonometric and hyperbolic trigonometric functions have been used to represent the obtained closed form traveling wave solutions. Furthermore, here, we reveal that the EMSE technique is a suitable, significant, and dominant mathematical tool for finding the exact traveling wave solutions for various FONLEEs in mathematical physics. We draw some 3D, 2D, and contour plots to describe the various wave behaviors and analyze the physical consequence of the attained solutions. Finally, we make a numerical comparison of our obtained solutions and other analogous solutions obtained using various techniques.