This paper represents the influences of temperature and hydrostatic pressure variations on GaAs/AlGaAs multiple quantum well slow light systems based on coherence population oscillations. An analytical model in non-integer dimension space is used to study the considerable effects of these parameters on optical properties of the slow light apparatus. Exciton oscillator strength and fractional dimension constants have special roles on the analytical model in fractional dimension. Hence, the impacts of hydrostatic pressure and temperature on exciton oscillator strength and fractional dimension quantity are investigated theoretically in this paper. Based on the achieved results, temperature and hydrostatic pressure play key roles on optical parameters of the slow light systems, such as the slow down factor and central energy of the device. It is found that the slope and value of the refractive index real part change with alterations of temperature and hydrostatic pressure in the range of 5-40 deg of Kelvin and 1 bar to 2 kbar, respectively. Thus, the peak value of the slow down factor can be adjusted by altering these parameters. Moreover, the central energy of the device shifts when the hydrostatic pressure is applied to the slow light device or temperature is varied. In comparison with previous reported experimental results, our simulations follow them successfully. It is shown that the maximum value of the slow down factor is estimated close to 5.5×104 with a fine adjustment of temperature and hydrostatic pressure. Meanwhile, the central energy shift of the slow light device rises up to 27 meV, which provides an appropriate basis for different optical devices in which multiple quantum well slow light is one of their essential subsections. This multiple quantum well slow light device has potential applications for use as a tunable optical buffer and pressure/temperature sensors.