Monotone traveling wave solutions of Mackey–Glass reaction diffusion equation with delayed diffusion term

Abstract This work investigates the existence of solutions to the Mackey–Glass equation, incorporating delays in both the diffusion and birth functions. This equation, a nonlinear functional differential equation, plays a significant role in modeling phenomena in biology and physiology. Using the monotone iteration method, we construct quasi-upper and quasi-lower solutions to rigorously establish the existence of solutions. The analysis relies on a modified Perron’s theorem.