Gravitational Lensing Signatures of Hayward-like Black Holes

We examine the gravitational lensing signatures of a Hayward-like regular black hole and its potential observational distinction from a Schwarzschild black hole. In the weak-field limit, the deflection angle includes a small positive correction proportional to $m \ell^2/b^3$, indicating slightly stronger light bending than in Schwarzschild, though the effect remains observationally negligible at large impact parameters. Current galaxy-scale Einstein-ring data, such as from ESO325-G004, cannot yet constrain the regular-core scale $\ell$. In the strong-deflection regime, for Sgr A* and M87*, the asymptotic position $\theta_{\infty}$ is identical to Schwarzschild's. Nevertheless, $\ell$ modifies strong-lensing coefficients $\bar a, \bar b$, influencing angular separations s, relative flux ratio $r_\mathrm{mag}$, and time delays $\Delta T_{2,1}$. Our predicted values for these observables remain consistent with current data, suggesting that future high-precision measurements of strong-field lensing may distinguish Hayward-like from Schwarzschild black holes.