Active Galactic Nuclei (AGN) with relativistic jets of plasma represent the most powerful persistent sources in the Universe. Their broad-band electromagnetic emission, from radio to gamma rays, is attributed to the radiative processes of particles accelerated in their jets. In order to describe this emission, models with a minimum of 7 parameters are commonly adopted: some representing physical quantities related to the jet, others providing a simple analytical parameterisation of the energy distribution of the accelerated particles. We will solve the differential equation describing the particles’ acceleration and radiation, thus obtaining “physical” (rather than “analytical”) particle distributions and reducing the number of model parameters. We will try to solve the differential equations analytically, complementing our work with the sympy python package for symbolic mathematics, and with numerical methods - if necessary. We will fit the radiation produced by the “physical” particle distributions to archival measurements at different wavelengths of a few selected active galaxies. The radiation of the particles accelerated in the AGN will be computed and fitted to the measurements with the agnpy python package.