In this paper, we study a fractional-order Keller–Segel coupled system focusing on their dynamic behavior and nonlinear wave structures. The Caputo–Fabrizio fractional derivative is used. This derivative has a non-singular kernel. It is suitable for real physical problems. The homotopy perturbation transform method (HPTM) is applied. The method provides an efficient semi-analytical solution. It avoids linearization and discretization. The solution is obtained in series form. The convergence of the solution is smooth and rapid. The dynamic behavior of the system is analyzed. The effect of different fractional orders \(\alpha\) is examined. Two-dimensional 2D graphs are plotted for various \(\alpha \in (0,1)\) values. Three-dimensional 3D surfaces are also presented. These graphs show the evolution of the solution clearly. Nonlinear wave structures are observed. The amplitude and shape of waves change with \(\alpha\). The results show that fractional order plays a key role. The proposed method is simple and accurate. It can be used for many nonlinear fractional models.