Abstract
Here, A new fractional sub-equation method is proposed for constructing the exact solutions of space-time fractional partial differential equations arising in nonlinear dynamics of microtubules in the sense of modified Riemann-Liouville derivative, which is the fractional version of the known method. The proposed approach is efficient and powerful for solving wide classes of nonlinear evoluation fractional order equations. It is observed that the performance of the proposed method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order. The solutions obtained here are new and have not been reported in former literature.