Title Exact solitary optical wave solutions and modulational instability of the truncated ˝−fractional Lakshamanan–Porsezian–Daniel model with Kerr, parabolic, and anti‑cubic nonlinear laws Type Article Keywords Not Record Abstract Not Record Researchers Jamilu Sabi’u (First researcher) , Prakash Kumar Das (Second researcher) , Arash Pashrashid (Third researcher) , hadi rezazadeh (Fourth researcher)