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We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing thestandard partial derivatives by the Dunkl derivatives in the standardKlein--Gordon (KG) equation. We show that the generalization with Dunklderivative of the $z$-component of the angular momentum is what allows theseparation of variables of the DKG equation. Then, we compute the energyspectrum and eigenfunctions of the DKG equations for the 2D Coulomb potentialand the Klein--Gordon oscillator analytically and from an ${\rm su}(1,1)$algebraic point of view. Finally, we show that if the parameters of the Dunklderivative vanish, the obtained results suitably reduce to those reported inthe literature for these 2D problems.

Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb Potential and the Klein--Gordon Oscillator