The peristaltic flow of Carreau nanofluid with heat and mass transfer through porous medium inside a symmetric horizontal channel with flexible walls is investigated. The Hall currents with viscous dissipation, heat absorption and chemical reaction are considered, the system is stressed by a uniform strong magnetic field. The problem is modulated mathematically by a system of non-linear PDE which describe the motion, heat and nanoparticles phenomenon of the fluid. These equations with subjected boundary conditions are transferred to a dimensionless form and simplified under the assumptions of long wavelength and low Reynolds number, then solved analytically by using perturbation technique for small Weissen-berg number. In other word these equations are solved also numerically by using Runge-Kutta-Merson method with Newton iteration in a shooting and matching technique. The effects of the emerging physical parameters of the problem on the velocity, temperature, and nanoparticles phenomena are discussed numerically for both techniques used for solutions and illustrated graphically through a set of figures. It is found that this problem plays a dramatic role in controlling the solutions. A comparison between the obtained solutions from both methods is made.