M-truncated fractional optical solitons and other periodic wave structures with Schrödinger–Hirota equation

In this article, some novel optical and periodic wave structures are studied to the fractional Schrödinger–Hirota equation with a truncated [Formula: see text]-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.