  The main goal of this article is to show a new method to solve some
Fractional Order Integral Equations (FOIE), more precisely the ones which are
linear, have constant coefficients and all the integration orders involved are
rational. The method essentially turns a FOIE into an Ordinary Integral
Equation (OIE) by applying a suitable fractional integral operator.
  After discussing the state of the art, we present the idea of our
construction in a particular case (Abel integral equation). After that, we
propose our method in a general case, showing that it does work when dealing
with a family of "additive" operators over a vector space. Later, we show that
our construction is always possible when dealing with any FOIE under the
above-mentioned hypotheses.
  Furthermore, it is shown that our construction is "optimal" in the sense that
the OIE that we obtain has the least possible order.
