This study investigates the free vibration behavior of porous functionally graded nanobeams composed of ferroelectric barium-titanate (BaTiO$_3$) and magnetostrictive cobalt-ferrite (CoFe$_2$O$_4$). Four different porosity models—uniform porosity (UPM), symmetric porosity (SPM), porosity concentrated in the bottom region (BPM), and porosity concentrated in the top region (TPM)—are considered. The nanobeam's constitutive equation calculates strains based on classical mechanical stress, thermal expansion, magnetostrictive and electroelastic properties, and nonlocal elasticity. The study examines the effects of various factors, including thermal stress, thermo-magneto-electroelastic coupling, electric and magnetic field potential, nonlocal features, porosity models, and changes in porosity volume, on the free vibration of the nanobeams. The temperature-dependent mechanical properties of BaTiO$_3$ and CoFe$_2$O$_4$ are also explored for the first time. The results show that the dimensionless frequencies are influenced by the nonlocal parameter, external electric potential, and temperature, causing them to increase, while the slenderness ratio and external magnetic potential cause them to decrease. The porosity volume ratio has different effects on frequencies depending on the porosity model. The study contributes to the understanding of the behavior of smart materials in nanoelectromechanical systems and other applications.This study investigates the free vibration behavior of porous functionally graded nanobeams composed of ferroelectric barium-titanate (BaTiO$_3$) and magnetostrictive cobalt-ferrite (CoFe$_2$O$_4$). Four different porosity models—uniform porosity (UPM), symmetric porosity (SPM), porosity concentrated in the bottom region (BPM), and porosity concentrated in the top region (TPM)—are considered. The nanobeam's constitutive equation calculates strains based on classical mechanical stress, thermal expansion, magnetostrictive and electroelastic properties, and nonlocal elasticity. The study examines the effects of various factors, including thermal stress, thermo-magneto-electroelastic coupling, electric and magnetic field potential, nonlocal features, porosity models, and changes in porosity volume, on the free vibration of the nanobeams. The temperature-dependent mechanical properties of BaTiO$_3$ and CoFe$_2$O$_4$ are also explored for the first time. The results show that the dimensionless frequencies are influenced by the nonlocal parameter, external electric potential, and temperature, causing them to increase, while the slenderness ratio and external magnetic potential cause them to decrease. The porosity volume ratio has different effects on frequencies depending on the porosity model. The study contributes to the understanding of the behavior of smart materials in nanoelectromechanical systems and other applications.