The present article reports the study of local anisotropic effects on Durgapal's fourth model in the context of gravitational decoupling via the minimal geometric deformation approach. To achieve this, the most general equation of state relating the components of the theta-sector is imposed to obtain the decoupler function f(r). In addition, certain properties of the obtained solution, such as the behavior of the salient material content threading the stellar interior; causality and energy conditions; hydrostatic balance through the modified Tolman-Oppenheimer-Volkoff conservation equation and stability mechanism against local anisotropies using the adiabatic index; sound velocity of the pressure waves; convection factor; and the Harrison-Zeldovich-Novikov procedure, are investigated to check whether the model is physically admissible or not. Regarding the stability analysis, it is found that the model presents unstable regions when the sound speed of the pressure waves and convection factor are used in distinction with the adiabatic index and Harrison-Zeldovich-Novikov case. To produce a more realistic picture, the numerical data for some known compact objects were determined and different values of the parameter alpha were considered to compare with the GR case, i.e., alpha = 0.