S-Asymptotically Periodic Solutions for Time-Space Fractional Evolution Equation.

This paper discusses the abstract time-space fractional evolution equation with the Caputo derivative of order α ∈ (0 , 1) and fractional power operator - A β , β ∈ (0 , 1) , where - A generates a C 0 -semigroup on a Banach space. The compactness and exponential stability of the semigroup which is generated by fractional power operator - A β are investigated. With the aid of the properties of the semigroup, the existence and global asymptotic behavior of S-asymptotically periodic solutions are obtained by some fixed point theorems and related inequalities. An example to the time-space fractional diffusion equation with fractional Laplacian will be shown. [ABSTRACT FROM AUTHOR]