Analytical approach for time-fractional Sharma-Tasso-Olver equation with non-singular kernel

This work considers a time-fractional Sharma-Tasso-Olver (STO) equation that describes the propagation of nonlinear dispersive waves in inhomogeneous media. The Atangana-Baleno derivative in the Caputo sense is used to develop the fractional derivative and a robust q-homotopy analysis Shehu transform method is being explored in this study. The existence and uniqueness of the obtained solution are discussed via Banach’s fixed point theory and also study the convergence analysis of the problem. The numerical outcomes are compared with with those obtained from Petrov-Galerkin method, and exact solutions to test the accuracy and the efficiency of the proposed method.