In this article, we employ the three coupled nonlinear Maccari’s-system with complex structure which describes the motion of isolated waves, localized in a small part of space. The new exact and solitary wave solutions of this model are obtained using the modified extended tanh-function method which built on the balance rule. The obtained results give a good interpretation for the propagation of these isolated waves. A comparison between our result and that obtained in previous work is listed. The constructed method can be applied to many other nonlinear fractional evolution equations.