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A CPW slot loop fed Minkowski shaped fractal dielectric resonator antenna is proposed. Self similar property of fractal geometry is utilized to bring higher order modes close together to realize a wide impedance bandwidth. A comparative study of the resonant frequency behavior between the well established fractal electrical boundary antennas and fractal magnetic boundary antennas is presented to provide insight into the functionality of the proposed antenna. The comparison highlights the fact that electrical boundary lowers resonance frequency, whereas fractal magnetic boundary increases the resonant frequency. Minkowski fractal is also compared with Koch fractal and Sierpinski curve geometries. It is observed that the Minkowski fractal DRA yields the widest impedance bandwidth along with stable gain amongst the three proposed geometries. The proposed antenna exhibits a fractional bandwidth of 64% (5.52 -10.72 GHz) and a maximum gain of 4.9 dBi.