Blazars are a type of active galactic nuclei that exhibit highly variable, non-thermal emission across the electromagnetic spectrum. This study presents an expanding emission model to investigate the physical processes leading to the blazar multi-wavelength emission. We explore the role of external photon fields in producing their high-energy emission and study the particle acceleration timescale to model their flaring activity. We aim to investigate the correlations between the flux at different wavelengths to gain insight into the physical properties of these intriguing astrophysical objects.