  This paper is concerned with a Lotka-Volterra type competition model with
free boundaries in time-periodic environment. One species is assumed to adopt
nonlocal dispersal and the other one adopts mixed dispersal, which is a
combination of both random dispersal and nonlocal dispersal. We show that this
free boundary problem with more general growth functions admits a unique
solution defined for all time. A spreading-vanishing dichotomy is obtained and
criteria for spreading and vanishing are provided. Moreover, under the weak
competition condition we provide the long-time asymptotic behavior of solution
when spreading occurs.
