For one-sided absorbing boundaries on the semi-infinite line, the first-passage time density scales as t to the power of -1/(2α)-1 at long times, with an optimal α minimizing the mean first-passage time.
On the other hand, the expected FPT of the L´ evy flight on the half-line is divergent for all 0< α≤1
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First-Passage Times for the Space-Fractional Spectral Fokker-Planck Equation
For one-sided absorbing boundaries on the semi-infinite line, the first-passage time density scales as t to the power of -1/(2α)-1 at long times, with an optimal α minimizing the mean first-passage time.