On Some Novel Soliton Structures for the Beta-Time Fractional Benjamin–Ono Dynamical Equation in Fluids

This paper consists of an exploration of the wave structures of the Benjamin–Ono equation along with a β-time fractional derivative. The model concerned is utilized to demonstrate internal waves of deep-stratified fluids. Bright, rational, periodic, and many more kinds of solutions for waves are achieved by utilizing the extended sinh-Gordon equation expansion (EShGEE) technique and the improved G′/G-expansion scheme. An influence of fractional-order derivatives was also explored which gives the non-existing results. The Mathematica tool is utilized to gain and verify the results. The results are represented by 3-D, 2-D, and contour graphs. A stability analysis is utilized to confirm that results are precise as well as exact. Modulation instability (MI) is also performed for the steady-state solutions to the concerned model.