Abstract
In this work, the coupled fractional nonlinear Hirota equation is defined by using a powerful fractional derivative sense, which is M-truncate derivative. We explore the fractional functional method and fractional simple equation method to investigate the structure of the solutions of the coupled fractional nonlinear Hirota equations, and some new periodic solutions and solitary wave solutions are successfully acquired. The two proposed approaches are simple, effective and direct. Moreover, some 3D and 2D graphs are sketched to elaborate the behavior of these solutions. These obtained solitary wave and periodic solutions are helpful to improve the understanding of the physical behavior of the corresponding mathematical model.
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