Analytical solutions to the fractional lakshmanan-porsezian-daniel model

A new local fractional-order derivative operator is introduced and the Lakshmanan–Porsezian–Daniel (LPD) model is interpreted via this operator. New analytical solutions to the LPD equation is presented by Jacobi elliptic functions and an anzätz method. The complex-valued LPD equation includes a nonlinear term which is considered from three diferent cases: Kerr, parabolic and anti-cubic law of nonlinearities. For each case, dark, bright, singular optical soliton solutions related with optical fbers are presented. Simulations representing behavior of these solutions for diferent parameter values are provided.