Comprehensive dynamic-type multi-soliton solutions to the fractional order nonlinear evolution equation in ocean engineering

Nonlinear fractional partial differential equations can explain a vast scope of engineering and science, like atomic physics, wireless transmission, nonlinear optics, acoustics, economics, materials science, control theory, plasma physics, quantum plasma in mechanics, biological systems of nonlinear case and so on. In this study, the new generalized $(G\prime /G)$-expansion technique have been studied for examine the nonlinear fractional equations and built exact analytical traveling as well as solitary wave solutions namely space–time one-dimensional fractional wave equation used to simulate wave transmission in a nonlinear medium with blending and space–time fractional regularized long wave equation enables bore expansion and wave generating in nonlinear model of solitary waves, ion acoustic plasma waves, shallow waves in water, and nonlinear dispersive waves with the help of conformable derivatives. The creatable equations are transformed into ordinary differential equations by fractional complex transformation. Some dynamical wave shapes of multiple solitons, single soliton, periodic anti-kink, anti-kink, flat-kink type solitary wave models have been created, and 3D, and contour have been built to represent these solutions. The results are expressed using hyperbolic, rational functions, and trigonometric and Maple or Mathematica utilized to graphically represent the obtained solutions. It is essential to point out that all resultant solutions are directly compared to the original solutions to ensure their exactness. The new generalized $(G\prime /G)$-expansion method is an operative, compatible, and fruitful approach for analyzing nonlinear fractional traveling waves.