  The goal of this work is to discuss how should we impose initial values in
fractional problems to ensure that they have exactly one smooth unique
solution, where smooth simply means that the solution lies in a certain
suitable space of fractional differentiability. For the sake of simplicity and
to show the fundamental ideas behind our arguments, we will do this only for
the Riemann-Liouville case of linear equations with constant coefficients.
  In a few words, we study the natural consequences in fractional differential
equations of the already existing results involving existence and uniqueness
for their integral analogues, in terms of the Riemann-Liouville fractional
integral. Under this scope, we derive naturally several interesting results.
One of the most astonishing ones is that a fractional differential equation of
order $\beta>0$ with Riemann-Liouville derivatives can demand, in principle,
less initial values than $\lceil \beta \rceil$ to have a uniquely determined
solution. In fact, if not all the involved derivatives have the same decimal
part, the amount of conditions is given by $\lceil \beta - \beta_* \rceil$
where $\beta_*$ is the highest order in the differential equation such that
$\beta-\beta_*$ is not an integer.
