  We consider a forager diffusing via a fractional heat equation and we
introduce several efficiency functionals whose optimality is discussed in
relation to the L\'evy exponent of the evolution equation.
  Several biological scenarios, such as a target close to the forager, a sparse
environment, a target located away from the forager and two targets are
specifically taken into account.
  The optimal strategies of each of these configurations are here analyzed
explicitly also with the aid of some special functions of classical flavor and
the results are confronted with the existing paradigms of the L\'evy foraging
hypothesis.
  Interestingly, one discovers bifurcation phenomena in which a sudden switch
occurs between an optimal (but somehow unreliable) L\'evy foraging pattern of
inverse square law type and a less ideal (but somehow more secure) classical
Brownian motion strategy.
  Additionally, optimal foraging strategies can be detected in the vicinity of
the Brownian one even in cases in which the Brownian one is pessimizing an
efficiency functional.
