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Two different antennas constructed using a new concept, the slot meander patch (SMP) design, are presented in this study. SMP antennas are designed for fourth-generation long-term evolution (4G LTE) handheld devices. These antennas are used for different target specifications: LTE-Time Division Duplex and LTE-Frequency Division Duplex (LTE TDD and LTE FDD). The first antenna is designed to operate in a wideband of 1.68-3.88 GHz to cover eight LTE TDD application frequency bands. Investigations have shown that the antenna designed with unequal meander widths has a higher efficiency compared to its equivalent antenna design with equal meander widths. The second antenna was configured as a multiband SMP antenna, which operates at three distinct frequency bands (0.5-0.75, 1.1-2.7, and 3.3-3.9 GHz), to cover eight LTE FDD application bands including the lowest and the highest bands. There is a good agreement between the measurement and simulation results for both antennas. Moreover, parametric studies have been carried out to investigate the flexible multiband antenna. Results have shown that the bandwidths can be improved through adjusting the meander widths without changing the SMP length and all other parameters.