  In this paper, the absorption of a particle undergoing L\'{e}vy flight in the
presence of a point sink of arbitrary strength and position is studied. The
motion of such a particle is given by a modified Fokker-Planck equation whose
exact solution in the Laplace domain can be described in terms of the Laplace
transform of the unperturbed (absence of the sink) Green's function. This
solution for the Green's function is a well-studied, generic result which
applies to both fractional and usual Fokker-Planck equations alike. Using this
result, the propagator and the absorption time distribution are obtained for
free L\'{e}vy flight and L\'{e}vy flight in linear and harmonic potentials in
the presence of a delta function sink, and their dependence on the sink
strength is analyzed. Analytical results are presented for the long-time
behaviour of the absorption time distribution in all the three above mentioned
potentials. Simulation results are found to corroborate closely with the
analytical results.
