Interaction solutions of high-order breathers and lumps for a (3+1)-dimensional conformable fractional potential-YTSF-like model

Abstract In this study, the breather solutions and interaction solutions for the (3+1)-dimensional conformable fractional potential Yu-Toda-Sasa-Fukuyama-like model are conducted. The fractional derivative is described using the conformable derivative. By using certain commutative methods, we derived the breather solutions and the interaction solutions of breathers and lumps in terms of Gramian. Solutions of these forms have never been studied. The features of the solutions were examined. Each interval of the breather has one and only one peak as well as trough, and the interaction between the breather wave and the breather wave or the lump wave is elastic. In addition, the effect of a fractional order change on the shape of the breathers is discussed through 3-dimensional images, and this change is able to be reduced to integer order and different fractional order.