  It is well known that, under standard assumptions, initial value problems for
fractional ordinary differential equations involving Caputo-type derivatives
are well posed in the sense that a unique solution exists and that this
solution continuously depends on the given function, the initial value and the
order of the derivative. Here we extend this well-posedness concept to the
extent that we also allow the location of the starting point of the
differential operator to be changed, and we prove that the solution depends on
this parameter in a continuous way too if the usual assumptions are satisfied.
Similarly, the solution to the corresponding terminal value problems depends on
the location of the starting point and of the terminal point in a continuous
way too.
