  We consider a Markovian jumping process with two absorbing barriers, for
which the waiting-time distribution involves a position-dependent coefficient.
We solve the Fokker-Planck equation with boundary conditions and calculate the
mean first passage time (MFPT) which appears always finite, also for the
subdiffusive case. Then, for the case of the jumping-size distribution in form
of the L\'evy distribution, we determine the probability density distributions
and MFPT by means of numerical simulations. Dependence of the results on
process parameters, as well as on the L\'evy distribution width, is discussed.
