  In this document, as far as the authors know, an approximation to the zeros
of the Riemann zeta function has been obtained for the first time using only
derivatives of constant functions, which was possible only because a fractional
iterative method was used. This iterative method, valid for one and several
variables, uses the properties of fractional calculus, in particular the fact
that the fractional derivatives of constants are not always zero, to find
multiple zeros of a function using a single initial condition. This partly
solves the intrinsic problem of iterative methods that if we want to find N
zeros it is necessary to give N initial conditions. Consequently, the method is
suitable for approximating nontrivial zeros of the Riemann zeta function when
the absolute value of its imaginary part tends to infinity. The deduction of
the iterative method is presented, some examples of its implementation, and
finally 53 different values near to the zeros of the Riemann zeta function are
shown.
