New Soliton Solutions for Fractional Spatio–Temporal Lakshmanan–Porsezian–Daniel Equation with Parabolic Law of Nonlinearity

The paper deals with the fractional spatio-temporal Lakshmanan-Porsezian-Daniel equation, where the nonlinearity terms consider in parabolic law. The governing model is reduced to an integer-order ordinary differential equation via a complex traveling wave transformation. We analyze the dynamic behavior and the gained phase portrait to ensure the existence of traveling wave solutions for the proposed model. A bright soliton solution for the fractional spatiotemporal Lakshmanan-Porsezian-Daniel equation will be constructed. In addition, kink soliton solution is also will obtained. We depicted the established solutions, in 2 and 3-dimensions, to understand their characteristics of naturality.