Abstract
In this article, a new generalized exponential rational function method (GERFM) is employed to extract new solitary wave solutions for the ionic currents along microtubules dynamical equations, which is very interested in nanobiosciences. In this article, the stability of the solutions is also studied. As a result, a variety of solitary waves are obtained with free parameters such as periodic wave solution and dark and bright solitary wave solutions. The solutions are plotted and used to describe physical phenomena of the problem. The work shows the power of GERFM. We found that the proposed method is reliable and effective and gives analytical and exact solutions.