Abstract
In this study, we implement three efficient integration algorithms to retrieve the solutions of optical soliton spacetime fractional nonlinear equation for the dynamics of microtubules MTs, which considered as one of the most important part in cellular processes biology. In this work we used three integration methods, firstly, the method of exp(-Omega)-expansion equation function, secondly the Kudryashov equation method in the general case and the method of extended Bernoulli sub-equation function, with the help of the fractional complex transformation and conformable derivatives which including the solution of complex function, rational function, hyperbolic function and exponential function. Finally, our results give good solution and understanding of the properties of the non-linear waves in fractional medium.