Testing regular scale-dependent black hole space time using particle dynamics: Shadow and gravitational weak lensing

In this study, we examine the effects of weak gravitational lensing and determine the shadow radius around black holes within the regular scale-dependent spacetime, also accounting for both uniform and nonuniform plasma models. By analyzing various gravitational lens, we compare corrections to vacuum lensing due to gravitational effects within plasma and plasma inhomogeneity, finding that these effects could be observed in hot gas within galaxy clusters. Starting with the orbits of photons around a regular scale-dependent black hole, we investigate the shadow and weak gravitational lensing phenomena. Utilizing observational data from the Event Horizon Telescope (EHT) for SgrA*, we constrain on parameter within regular scale-dependent gravity. To connect our findings to observations, we examine the magnification and positioning of lensed images, along with the weak deflection angle and magnification for sources near different galaxies.