In this equation, Δ Δ x and Δ Δ p denote the uncertainties in position and momentum, respectively. The term ℏ ℏ represents the reduced Planck constant, while β β is a parameter that embodies the minimal length scale predicted by the GUP. The GUP is more than a theoretical curiosity; it signifies a cornerstone concept in the pursuit of unifying quantum mechanics with general relativity. It posits an absolute minimum uncertainty in the position of particles, approximated by the Planck length, underscoring its significance in the realms of quantum gravity and string theory where such minimal length scales are anticipated. Various quantum gravity theories, such as string theory, loop quantum gravity, and quantum geometry, propose a generalized version of the uncertainty principle (GUP), which suggests the presence of a minimum measurable length. In earlier research, multiple forms of the GUP have been introduced