Symmetry analysis, exact solutions, and conservation laws of time fractional reaction-diffusion system occurring in diffusive flows

In this study, we analyze the non-linear time fractional reaction-diffusion system of equations through the Lie symmetry analysis. Initially, we ascertain the symmetries associated with the physical model, and the given equation is reduced to a system of ordinary differential equations meticulously through one of the optimal algebra methods. Further, we construct an exact power series solution and studied the non-linear behavior of the solutions under the fractional derivatives. We also present the numerical simulation for the reduced system of equations, taking the initial conditions and isotonic condition into account. Furthermore, we illustrate the results graphically, underlying different physical and chemical phenomena. Finally, we present the non-classical symmetry and conservation laws.