A fractional-order predator–prey model (FOPPM) based on the Caputo derivative of order \(\alpha\) (\(0 < \alpha \le 1\)) is developed to examine the joint influence of a strong Allee effect in the prey and a nonlinear anti-predator feedback acting on the predator. The formulation couples cubic prey growth and bilinear predation with a saturating feedback loss, thereby representing threshold-dependent recovery, trophic conversion, and density-dependent behavioural regulation. The system admits three boundary equilibria, while coexistence equilibria are determined by a corrected cubic algebraic equation. Its discriminant classifies one- and three-real-root regimes, but ecological feasibility further requires \(A<X^*<K\), \(Y^*>0\), and \(kmX^*-d>0\). Nullcline geometry shows that at most two roots can be biologically feasible; the actual number is therefore established by direct root filtering for each parameter set. Local stability is characterised through the Jacobian \(\mathcal{J}(E^*)\) and the classical eigenvalue test for integer-order dynamics, while the fractional-order model requires satisfaction of Matignon’s criterion \(|\arg(\lambda_i)|>\frac{\alpha\pi}{2}, \; i=1,2.\) The coexistence equilibrium may switch between stability and instability under variations in carrying capacity \(K\), Allee threshold \(A\), interaction rate \(m\), or feedback intensity \(\varepsilon\). Because the Jacobian eigenvalues do not depend on \(\alpha\), fractional memory does not rotate them; instead, decreasing \(\alpha\) widens the admissible Matignon sector and changes the rate and shape of transient relaxation. A weighted population estimate establishes positivity, uniform boundedness, and global existence. Since the extinction equilibrium is always locally stable under a strong Allee effect, coexistence cannot be globally attractive on the entire positive quadrant. A Volterra-type logarithmic functional is therefore formulated as a basin-restricted Mittag–Leffler certificate on positively invariant sets separated from the coordinate axes. The theoretical results are tested with a fractional Adams–Bashforth–Moulton predictor–corrector (ABM–PC) scheme. A grid-refinement study gives observed orders \(1.91\), \(1.90\), and \(1.96\) for \(\alpha=0.9\), consistent with the expected order \(\min\{2,1+\alpha\}\). An independent \(\alpha=1\) comparison with a high-accuracy Runge–Kutta solution gives maximum componentwise errors below \(3.5\times10^{-4}\). Parameter sweeps across \((K,A,m,\varepsilon,\alpha)\) then quantify changes in feasibility, stability, and transient persistence. For \(\alpha=1\), a trace-zero crossing with positive determinant and transversality is the classical Hopf candidate. For \(0<\alpha<1\), crossing the Matignon boundary is instead a fractional stability-sector transition; it is not, by itself, a Hopf bifurcation. Moreover, autonomous Caputo systems of non-integer order do not possess exact nonconstant periodic solutions, so the computed oscillations are interpreted as memory-dependent transients rather than limit cycles. Overall, the FOPPM provides a coherent framework for studying memory, Allee thresholds, and behavioural feedback within one model. Corrected equilibrium algebra, explicit feasibility filtering, fractional stability theory, reproducible convergence checks, and regenerated simulations together distinguish true asymptotic conclusions from finite-time memory effects.
