In this study, a reaction mechanism proposed by Belousov and Zhabotinskii, which corresponds to many physical phenomena, from the complex wave behavior of the heart and various organs in our body to the formation of biological models that cause embryonic developments, was examined. We considered the derivative with the time evolution as the Riemann-Liouville derivative operator. Lie symmetry generators corresponding to the transformation groups in which our model remains invariant were constructed. The power series solution was systematically designed, including the convergence analysis of this system. Besides, conservation laws of the model were created for the 0 < alpha < 1 states of the a fraction order.