Probing variation of the fine-structure constant in runaway dilaton models using Strong Gravitational Lensing and Type Ia Supernovae

In order to probe a possible time variation of the fine-structure constant ($\alpha$), we propose new method based on Strong Gravitational Lensing and Type Ia Supernovae observations. By considering class dilaton runaway models, where $\frac{\Delta \alpha}{\alpha}= - \gamma \ln{(1+z)}$, obtain constraints \alpha}{\alpha}$ at level $\gamma \approx 10^{-2}$ ($\gamma$ captures physical properties model). Since data set covers redshift range $0.075 \leq z 2.2649$, derived here provide independent bounds $\alpha$ low, intermediate high redshifts.