Waveform flow of non-Newtonian fluid through a porous medium of the non-symmetric sloping canal under the effect of rotation and magnetic force, which has applied by the inclined way, have studied analytically and computed numerically. Slip boundary conditions on velocity distribution and stream function are used. We have taken the influence of heat and mass transfer in the consideration in our study. We carried out the mathematical model by using the presumption of low Reynolds number and small wave number. The resulting equations of motion, which are representing by the velocity profile and stream function distribution, solved by using the method of a domain decomposition analysis and we obtained the exact solutions of velocity, temperature, and concentration. The expressions of velocity, temperature, and concentration of the particles of the fluid have obtained and examined graphically by utilizing the soft wave of the Mathematica program. The efforts of various variables on mathematical modeling of motion and energy are discussed in detail. We found that.