The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real
initial condition is taken. In the present work, we explain an iterative method that is created using the fractional
calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the
space of complex numbers given a real initial condition, ...

The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real
initial condition is taken. In the present work, we explain an iterative method that is created using the fractional
calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the
space of complex numbers given a real initial condition, which allows us to find both the real and complex roots
of a polynomial unlike the classical Newton-Raphson method.

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