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.

中文翻译：

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分数效应对分数光学超材料中调制不稳定性和亮孤子的影响

在本文中，我们推导出了分数阶非线性薛定谔方程，它在非局部时间演化下对超材料中的脉冲传播进行建模。我们研究了分数效应对调制不稳定性 (MI) 增益和亮孤子的影响。负群速度 (GV) 是左手材料的必要特征之一。对于一些分数参数α观察到 GV 的负性。当一阶和二阶色散的符号相反时，就会出现 MI。结果表明，分数参数可以控制MI增益以及脉冲的幅度和宽度。