On the stability of some exact solutions to the generalized convection–reaction–diffusion equation

Stability of a set of traveling wave solutions to the convection–reaction–diffusion equation taking into account the effects of memory is studied by means of the qualitative methods and numerical simulation.

► We investigate stability properties of a set of traveling wave solutions to the convection–reaction–diffusion equation taking into account the effects of memory.
► We examine the analytical solution previously obtained within the direct method.
► Our analytical studies are backed by the numerical simulations.