We show that under particular circumstances a general relativistic spherically symmetric bounded distribution of matter could satisfy a non-local equation of state. This equation describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. We have found that these types of dynamic bounded matter configurations, with constant compactness or gravitational potentials at the surface, admit a conformal Killing vector field and fulfil the energy conditions for anisotropic imperfect fluids. We present several analytical and numerical models satisfying these equations of state which collapse as reasonable radiating anisotropic spheres in general relativity.