# Analytical solution of local fractional Klein-Gordon equation for the generalized Hulthen potential

## TL;DR

This paper derives exact analytical solutions for the one-dimensional fractional Klein-Gordon equation with a generalized Hulthen potential, exploring relativistic effects within conformable fractional calculus.

## Contribution

It provides the first analytical eigenvalues and eigenfunctions for the fractional Klein-Gordon equation with this potential using conformable fractional derivatives.

## Key findings

- Exact eigenvalues and eigenfunctions obtained
- Relativistic effects analyzed in fractional order context
- Fractional calculus offers a natural framework for these solutions

## Abstract

One dimensional Klein-Gordon (KG) equation is investigated in the domain of conformable fractional calculus for one dimensional scalar potential namely generalized Hulthen potential. The conformable fractional calculus is based on conformable fractional derivative which is the most natural definition in non integer order calculus. Fractional order differential equations can be solved analytically by means of this derivative operator. We obtained exact eigenvalue and eigenfunction solutions of local fractional KG equation and investigated the evolution of relativistic effects in correspondence with the fractional order.