<p>Vegetation ring patterns observed in clonal plant communities are often associated with plant-soil negative feedback mechanisms arising from the accumulation of toxic compounds in the soil. This study aims to develop and analyze a fractional-order mathematical model for vegetation ring formation driven by plant-soil negative feedback describing the spatiotemporal interaction between plant biomass and soil toxicity. Rigorous theoretical results on uniqueness, convergence, and Ulam–Hyers stability are established. Since an exact analytical solution of the coupled nonlinear system is not available, two semi-analytical techniques, namely the homotopy analysis method and the controlled picard transform technique, are employed to construct approximate series solutions. The use of these two independent approaches allows the obtained results to be cross-validated and enhances the reliability of the solution behavior. The obtained results demonstrate the effectiveness and consistency of both methods and highlight the potential of the proposed fractional-order framework for accurately describing vegetation pattern formation with ecological memory effects. To further illustrate the dynamics of the model, two- and three-dimensional graphical simulations are presented for different fractional orders. The results demonstrate the influence of memory effects on the formation and evolution of vegetation ring structures and provide deeper insight into the role of plant-soil feedback in spatial ecological dynamics.</p>