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 $D_{\xi }^{\alpha }G\left(\xi \right)/G\left(\xi \right)$ 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.

在此，提出了一种新的分数次方程方法，以构造改进的Riemann-Liouville导数意义上的微管非线性动力学产生的时空分数偏微分方程的精确解，这是已知的分数形式 $d_{\xi }^{\alpha }G（\xi ）/G（\xi ）$ 方法。

所提出的方法对于求解多种非线性演化分数阶方程是有效且强大的。可以看出，所提出方法的性能是可靠的，并且将用于为分数阶的任何其他NPDE建立新的一般封闭形式的解决方案。这里获得的解决方案是新的，以前的文献中没有报道过。