On the Speed of Spread for Fractional Reaction-Diffusion Equations

The fractional reaction diffusion equation +=()is discussed, where is a fractional differential operator on ℝ of order∈(0,2), the 1 function vanishes at =0 and =1, and either≥0 on (0,1) or <0 near =0. In the case of nonnegative g,it is shown that solutions with initial support on the positive half axisspread into the left half axis with unbounded speed if () satisfies someweak growth condition near =0 in the case >1, or if is merelypositive on a sufficiently large interval near =1 in the case <1. On the other hand, it shown that solutions spread with finite speed if(0)<0. The proofs use comparison arguments and a suitable familyof travelling wave solutions