New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ6 Method in Fractional Sense

This paper explores a significant fractional model, which is the fractional Lakshamanan–Porsezian–Daniel (FLPD) model, widely used in various fields like nonlinear optics and plasma physics. An advanced analytical solution for it is attained by the Φ6 technique. According to this methodology, effective and accurate solutions for wave structures within various types can be produced in the FLPD model framework. Solutions such as dark, bright, singular, periodic, and plane waves are studied in detail to identify their stability and behavior. Validations are also brought forward to assess the precision and flexibility of the Φ6 technique in modeling fractional models. Therefore, it is established in this study that the Φ6 technique represents a powerful tool for examining wave patterns in differential fractional order models.