DYNAMICAL BEHAVIOR OF SEMI-ANALYTICAL SOLUTIONS IN THE TIME-FRACTIONAL BENJAMIN–ONO EQUATION AND STABILITY ANALYSIS

This research presents the study of the time-fractional Benjamin-Ono equation (BOEs)with the support of Caputo-Fabrizio fractional derivative(CFFD). In the present work, thefractional homotopy perturbation transform (FHPTM) method has been taken to obtainsome new semi-analytical solution of the fractional BOE. The stability study of the modelwith Banach’s fixed-point t heory i s u sed i n a n i terative m anner. A fter t hat, w e providesome numerical examples to demonstrate the theoretical results that were attained. Lastly,a graphical representation of the results is given.