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In this article, some novel optical and periodic wave structures are studied to the fractional Schrödinger–Hirota equation with a truncated M -fractional derivative. For this purpose, the integration scheme, which was adopted is fractional extended Fan sub-equation. The optical solitons are observed in single and combined forms, and some other solutions are also fall out during the derivation. Subsequently, the exact solutions demonstrate the effectiveness, efficiency and reliability of the proposed methods, which can be useful for exploring various kind of solutions in the diverse fields of contemporary sciences and engineering. The constraint conditions are utilized, as well as the gained solutions are plugged into the model to verify the results. [ABSTRACT FROM AUTHOR]

In this article, some new traveling wave solutions to the space-time fractional equal-width equation are constructed with the help of the extended Fan sub-equation method. A simple transformation is introduced to convert the fractional order partial differential equation into an ordinary differential equation. As a result, the bright, dark, singular and combined wave solitons are observed for different values of two parameters. Moreover, the graphical representations are also depicted. [ABSTRACT FROM AUTHOR]