New structures for the space-time fractional simplified MCH and SRLW equations

Highlights: • New solitary structures for the space-time fractional simplified MCH and SRLW are constructed. • The space and time fractional orders involve are in the sense of the new conformable fractional derivative. • The modified extended tanh method is adopted due its various advantages. • The method provides exact travelling wave solutions of hyperbolic and trigonometric functions type, respectively. - Abstract: In this paper, we constructed new solitary structures for the space-time fractional simplified modified Camassa-Holm (MCH) equation and space-time fractional symmetric regularized long wave (SRLW) equation using the modified extended tanh method. The space-time fractional derivatives are defined in the sense of the new conformable fractional derivative. Further, with the help of Mathematica software, the set of over-determined algebraic equations obtained after reducing the equations to ordinary differentials equations are treated. We finally provide graphical illustrations for some structures.