The properties of the deformed bosonic oscillator, and the quantum groups Uq(SL(2)) and GLq(2) in the limit as their deformation parameter q goes to a root of unity are investigated and interpreted physically. These properties are seen to be related to fractional supersymmetry and intrinsic anyonic spin. A simple deformation of the Klein-Gordon equation is introduced, based on GLq(2). When q is...

this paper studies the perturbed klein-gordon equation by the aid of several methods of integrability. there are six forms of nonlinearity that are considered in this paper. the parameter domains are thus identified.

We propose a covariant definition of the fractional Klein-Gordon equation with long-range interactions independent metric underlying manifold. As an example we consider on AdS$_{2+1}$, computing explicit kernel representation Laplace-Beltrami operator as well two-point propagator equation. Our results suggest that only exists if mass is small compared to inverse AdS radius, presumably because s...

The modified decomposition method has been implemented for solving a coupled Klein-Gordon Schrödinger equation. We consider a system of coupled Klein-Gordon Schrödinger equation with appropriate initial values using the modified decomposition method. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions of coupled Klein-Gordon Schr...

In this paper we prove standard and reversed Strichartz estimates for the Klein--Gordon equation in $\mathbb{R}^{3+1}$. Instead of Fourier theory, our analysis is based on fundamental solutions free equations fractional integrations. final part paper, apply study a semilinear equation.

In this paper we consider a fractional wave equation for hypoelliptic operators with singular mass term depending on the spacial variable and prove that it has very weak solution. Such analysis can be conveniently realised in setting of graded Lie groups. The uniqueness solution, consistency classical solution are also proved, under suitable considerations. This extends improves results obtaine...