The fractional reaction diffusion equation is discussed, where is a fractional differential operator on of order , the function vanishes at and , and either on or near . In the case of nonnegative g, it is shown that solutions with initial support on the positive half axis spread into the left half axis with unbounded speed if satisfies some weak growth condition near in the case , or if is merely positive on a sufficiently large interval near in the case . On the other hand, it shown that solutions spread with finite speed if . The proofs use comparison arguments and a suitable family of travelling wave solutions.
Hans Engler. "On the Speed of Spread for Fractional Reaction-Diffusion Equations." Int. J. Differ. Equ. 2010 (SI1) 1 - 16, 2010. https://doi.org/10.1155/2010/315421