Average time spent by Lévy flights and walks on an interval with absorbing boundaries

The problems of Levy flights and Levy walks on a finite interval with absorbing boundaries were discussed. The Fredholm integral equations and Laplace transform in the temporal domain were used for the solution of mean time of travel before absorption for discrete Levy flights and Levy walks. The fractional differential equations were shown to be good approximations for Levy flights with absorbing boundaries for α>2. It was also shown that these approximations break down in the vicinity of the boundaries when α=2.