In this work, we propose a new model concerning emphatically coupled nerve fibers. Through the fractional complex transformation and the improved Riccati equation mapping method, various exact traveling wave solutions for the considered model are derived. In our resolution, we introduce the non-integer derivative for the description of long memory and hereditary properties of various materials. These phenomena have not yet been taken in account in the previous works. This memory effect can be used to describe some unknown phenomena observed during the propagation of impulses in myelinated fibers.
