On an initial-boundary-value problem for a coupled, singular reaction-diffusion system arising from a model of fractional-order chemical autocatalysis with decay

In this paper we examine a coupled system of singular reaction-diffusion equations arising as a model of isothermal chemical autocatalysis with termination in which the orders of autocatalysis and termination, m and n respectively, are fractional, that is, 0 n, k is sufficiently small and the initial input of the autocatalyst is sufficiently large. Here k is a parameter which measures the relative strength of the termination step to that of the autocatalysis. Further, a number of numerically corroborated conjectures concerning the structure of the travelling waves, and of solutions in the absence of travelling waves, are presented.