Search

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]