Traveling wavefronts for a time delayed non-Newtonian filtration equation

► The equation is a degenerate parabolic equation with time delay. ► The necessary and sufficient conditions to ensure the existence of traveling wavefronts are obtained. ► We show that the traveling wave may be a finite, semi-finite, or infinite traveling wave for different exponent. ► Accurate estimates of convergent rates of the semi-finite or infinite traveling waves are obtained.