Exact solutions of the 2D Dunkl–Klein–Gordon equation: The Coulomb potential and the Klein–Gordon oscillator

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