  Using the Riesz-Feller fractional derivative, we apply the factorization
algorithm to the fractional quantum harmonic oscillator along the lines
previously proposed by Olivar-Romero and Rosas-Ortiz, extending their results.
We solve the non-Hermitian fractional eigenvalue problem in the k space by
introducing in that space a new class of Hermite `polynomials' that we call
Riesz-Feller Hermite `polynomials'. Using the inverse Fourier transform in
Mathematica, interesting analytic results for the same eigenvalue problem in
the x space are also obtained. Additionally, a more general factorization with
two different Levy indices is briefly introduced
