The dynamical evolution of planetary and protoplanetary structures represents one of the major challenges for the modern Computational Astrophysics. The focus of our investigation is to study the dynamical evolution of a young planetary system both in isolation as well as embedded in a typical stellar open cluster. We simulate the whole system using the code GASPH (Pinto, Capuzzo-Dolcetta & Magni, 2019), an optimized SPH (Smoothed Particle Hydrodynamics) code which deals with self-gravity by mean of a tree-based scheme. Our young planetary system is composed by a central, solar like, star surrounded by a gaseous disk containing a fully formed Jovian planet. The disk is assumed as a marginally self-gravitating, ideal, gas and, to study its evolutionary properties, it is parameterized as an ensemble of SPH particles with an initial mass of 0.01 solar masses, essentially the value of the so called minimum solar mass nebula. We set our young planetary system in a typical open star cluster in order to study the gravitational perturbations induced by stellar flybys at varying the mass of the stellar perturber from 0.5 to 8 solar masses. We change the perturber periastron in the range of 100 - 500 AU and ,in order to investigate prograde and retrograde configurations, we vary its orbital inclination from 0 to 180 degrees. We followed the evolution of orbital planetary parameters like the semi-major axis and eccentricity. In addition, we investigated the accretion mass rate of the planet inside the disk, both during the stellar flyby and in the case without any external perturbation. In this frame, the dynamical evolution of the disk is quantified by the analysis of its Lagrangian radii. We confirmed the relevant role of the disk to catalyze the gravitational perturbation from the stellar perturber to the Jovian planet, converting the impulsive action of the stellar flyby to a softer long-time planet-disk interaction. We show the different role of retrograde and prograde perturber orbits for the dynamical evolution of a young planetary system in a stellar environment. Finally, our theoretical, simulative, study could be a support for exploratory astrophysics surveys in stellar clusters, aiming to the search of new young exoplanetary systems in such environments.