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In this document, as far as the authors know, an approximation to the zerosof the Riemann zeta function has been obtained for the first time using onlyderivatives of constant functions, which was possible only because a fractionaliterative method was used. This iterative method, valid for one and severalvariables, uses the properties of fractional calculus, in particular the factthat the fractional derivatives of constants are not always zero, to findmultiple zeros of a function using a single initial condition. This partlysolves the intrinsic problem of iterative methods that if we want to find Nzeros it is necessary to give N initial conditions. Consequently, the method issuitable for approximating nontrivial zeros of the Riemann zeta function whenthe absolute value of its imaginary part tends to infinity. The deduction ofthe iterative method is presented, some examples of its implementation, andfinally 53 different values near to the zeros of the Riemann zeta function areshown.

An approximation to zeros of the Riemann zeta function using fractional calculus