Kang‐Le Wang
The main purpose of this work is to explore the fractional Yajima–Oikawa equation with conformable fractional derivative. The fractional Yajima–Oikawa equation is an important model in physics, which is used to describe the ion sound waves under Langmuir action waves. First, the fractional travelling wave transformation is used to convert the fractional Yajima–Oikawa equation into an ordinary differential equation. The variational principle is constructed via the semi-inverse transformation method. Second, a plane dynamic system is obtained by adopting the Galilean transformation, and its Hamiltonian function, sensitivity, chaotic behavior and bifurcation analysis are presented. Finally, the model is investigated by utilizing two efficient mathematical methods, namely the novel fractional direct mapping method and the improved fractional [Formula: see text] expansion method. Some new soliton solutions and periodic solutions are successfully derived, which are extremely useful for further research on the corresponding physical phenomena. The physical characteristics of the obtained solutions are described by drawing some three-dimensional and two-dimensional graphs with proper parameter values.