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

The strategy of survival for a competition between normal and anomalous diffusion