Diverse solitary wave structures to the conformable time fractional equations through two powerful methods

In this paper, novel soliton solutions to the conformable time fractional Benjamin–Bona–Mahony and seventh-order time fractional Sawada–Kotera–Ito equations are investigated via application of two mathematical methods. These models are reformulated into a fractional order derivative by applying the conformable derivative operator. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic and exponential function solutions. For physical phenomena of concern models, some solutions are plotted in two-dimensional and three-dimensional by assigning the particular values to the parameters under the constrain conditions with the assistance of Mathematica software. Hence, all results obtained by our proposed methods are novel and have not been yet reported in any literature. Moreover, the proposed schemes are enormously superbly mathematical tools to review wave solutions of several fractional models in nonlinear science.