Abstract
In this paper, we study the soliton wave of the fractional Benjamin-Ono equation based on the extended simplest equation method. The accuracy of the obtained soliton wave solutions is investigated by comparing the obtained analytical and semi-analytical solutions. The semi-analytical solutions are constructed by applying the Adomian decomposition method. The semi-analytical method is used based on the constructed initial and boundary conditions from the obtained analytical solutions. Both solutions (analytical and semi-analytical) are plotted through different techniques for explaining the internal waves of deep-stratified fluids.