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By replacing the spatial derivative with the Dunkl derivative, we generalize the Fokker-Planck equation in (1+1) dimensions. We obtain the Dunkl–Fokker–Planck eigenvalues equation and solve it for the harmonic oscillator plus a centrifugal-type potential. Furthermore, when the drift function is odd, we reduce our results to those of the recently developed Wigner–Dunkl supersymmetry. [ABSTRACT FROM AUTHOR]

In this work we introduce two different generalizations of the Fokker–Planck equation in (1+1) dimensions by replacing the spatial derivatives in terms of generalized Dunkl-type derivatives involving reflection operators. As applications of these results, we solve exactly the generalized Fokker–Planck equations for the harmonic oscillator and the centrifugal-type potentials. • We generalize the Fokker–Planck equation through Dunkl-type derivatives. • We solve exactly the Dunkl–Fokker–Planck equation for the centrifugal-type potential. • We solve exactly the Dunkl–Fokker–Planck equation for the harmonic oscillator. • We compute the energy spectrum and eigenfunctions of these potentials. [ABSTRACT FROM AUTHOR]