  A model-free theoretical framework for a phenomenological description of
spin-lattice relaxation by anomalous translational diffusion in inhomogeneous
systems based on the fractional diffusion equation is developed. The dependence
of the spin-lattice relaxation time on the size of the pores in porous glass
Vycor is experimentally obtained and found to agree well with our theoretical
predictions. We obtain nonmonotonic behavior of the translational spin-lattice
relaxation rate constant (it passes through a maximum) with the variation of
the parameter referring to the extent of inhomogeneity of the system.
