  By integration of generalized BSBM and Brans-Dicke cosmological models, in
this article, we investigate the theoretical framework of fine structure
constant variation and current cosmic acceleration. We first develop a
mathematical formalism to analyse the stability of the model. By employing
observational data to constrain the model parameters, phase space is performed
and the attractor solutions of the model are detected. We then examine the
model against observational data such as observational Hubble parameter dataset
and quasar absorption spectra. The results confirms current universe
acceleration and also predicts fine structure constant variation. Furthermore,
extrapolation of the best fitted model in high redshift ($z> 15$) illustrates a
significantly larger variation of fine structure constant in earlier epoch of
the universe.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics