First passage times of Levy flights coexisting with subdiffusion

We investigate both analytically and numerically the first passage time (FPT) problem in one dimension for anomalous diffusion processes in which Levy flights and subdiffusion coexist. We analyze the FPT for three subclasses of Levy stable motions: (i) symmetric Levy motions characterized by Levy index mu, 0 < 2, and skewness parameter beta=0, (ii) one-sided Levy motions with mu, 0 < 1, and skewness beta=1, and (iii) two-sided skewed Levy motions, the extreme case, 1 < 2, and skewness beta=-1. In all three cases the waiting times between successive jumps are heavy tailed with index alpha. We show that in all three cases the FPT distributions are power laws. Our findings extend earlier studies on FPTs of Levy flights by considering the interplay between long rests and the Levy long jumps.