Abstract
The modeling of nonlinear dynamical models and their solutions have imperative values, whereas the soliton mathematical methods are favorable tools for analyzing such highly nonlinear practical problems. Herein, time-fractional coupled Burger's model is analyzed. Some solitary wave solutions, containing one-soliton, two-soliton, three-soliton and N-soliton, have been fetched using a modified sort of the well-known exp-function approach. Dominant effects of the fractional parameters have been illustrated and it is noted that the higher values of the fractional number cause a significant impact on the wave propagation. The one wave pattern for the u-component is quite identical, while an increase in the fractional parameter is producing an increment in the wave structure while a similar but opposite pattern is noted for the v-component. An increment in the wave structure is noted for higher values of the time-fractional parameter for both u- and v-components in the case of a two-wave solution. The benefits of the proposed computational code of the exp-function scheme are consistent, a general form of exact solutions, reduced computational complexity and stable and efficiently useful. The obtained solitary waves solutions will be a useful extension to the preceding results and greatly assist in clarifying the features of nonlinear waves in viscous flow.