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In this paper, we have derived the fractional nonlinear Schrödinger equation modeling pulse propagation in metamaterials under nonlocal time evolution. We have investigated the influence of the fractional effects on both modulational instability (MI) gain and bright soliton. A negative group velocity (GV) is one of the necessary characteristic signatures of a left-handed material. The negativity of GV is observed for some fractional parameters  α . MI occurs when the signs of first and second order dispersion are opposed. The results show that the fractional parameters can control the MI gain as well as the amplitude and the width of pulse.

Impact of fractional effects on modulational instability and bright soliton in fractional optical metamaterials