A note on “two-point boundary value problems associated with non-linear fuzzy differential equations”

In recent papers, Lakshmikantham et al. and O’Regan et al. assert that two-point boundary value problem for a fuzzy differential equation is equivalent to an integral equation and the proofs of the main results in the above cited papers use this equivalence. We prove by a counterexample that, by using H-differentiability or Hukuhara differentiability this assertion does not hold. Moreover, it is proved that a large class of two point boundary value problems have no solutions at all under H-differentiability or Hukuhara differentiability.