  In this paper, we study the competition of two diffusion processes for
achieving the maximum possible diffusion in an area. This competition, however,
does not occur in the same circumstance; one of these processes is a normal
diffusion with a higher growth rate, and another one is an anomalous diffusion
with a lower growth rate. The trivial solution of the proposed model suggests
that the winner is the one with the higher growth rate. But, the question is:
what characteristics and strategies should the second diffusion include to
prolong the survival in such a competition? The studied diffusion equations
correspond to the SI model such that the anomalous diffusion has memory
described by a fractional order derivative. The strategy promise that anomalous
diffusion reaches maximum survival in case of forgetting some parts of the
memory. This model can represent some of real phenomena, such as the contest of
two companies in a market share, the spreading of two epidemic diseases, the
diffusion of two species, or any reaction-diffusion related to real-world
competition.

Physics and Society