This study investigates new exact solutions of the time-fractional Benjamin–Ono equation by using the improved-F expansion method. Here, the time-fractional derivative is considered in terms of Conformable fractional derivative (CFD). At first, the fractional complex transform is used to convert the time-fractional Benjamin–Ono equation to an ordinary differential equation. Secondly, the proposed method has applied the given equation to construct exact solutions. Finally, all obtained analytical solutions are presented at the end of the paper.

中文翻译：

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改进的 F 扩展方法在时间分数本杰明-小野方程中的应用

本研究使用改进的 F 展开方法研究了时间分数本杰明 - 小野方程的新精确解。在这里，时间分数导数是根据可配分数阶导数 (CFD) 来考虑的。首先，分数阶复数变换用于将时间分数本杰明-奥诺方程转换为常微分方程。其次，所提出的方法应用给定的方程来构造精确解。最后，文末给出了所有得到的解析解。