Bio-impedance non-invasive measurement techniques usage is rapidly increasing in the agriculture industry. These measured impedance variations reflect tacit biochemical and biophysical changes of living and non-living tissues. Bio-impedance circuit modeling is an effective solution used in biology and medicine to fit the measured impedance. This paper proposes two new fractional-order bio-impedance plant stem models. These new models are compared among three commonly used bio-impedance fractional-order circuit models in plant modeling (Cole, Double Cole, FO Double-shell). The two proposed models represent the characterization of the biological cellular morphology of the plant stem through a non-invasive method. Experiments are conducted on two samples of three different medical plant species under the family Lamiaceae, and each sample is measured at two inter-electrode spacing distances. Bio-impedance measurements are done using an electrochemical station (SP150) in the frequency range from 100 Hz to 100 kHz. All employed models are compared by fitting the measured data to find the most suitable circuit model that models the plant stem. The proposed models give the best results in all inter-electrode spacing distances. Four different meta-heuristic optimization algorithms are used in the fitting process to extract all models parameter and find the best optimization algorithm in the bio-impedance problems.