M-derivative applied to the soliton solutions for the Lakshmanan–Porsezian–Daniel equation with dual-dispersion for optical fibers

Abstract

Optical dispersive soliton solutions for the fractional Lakshmanan–Porsezian–Daniel equation for optical fibers are studied in this paper considering the M-derivative of order $$\chi$$ . The analytical method considered here is based on the Jacobi elliptic function (JEF) anzatz method. We found new optical soliton solutions that are relevant for the dynamics inside optical fibers. Some constraints conditions arise between the parameters of the JEF soliton solutions. Typical behaviour of the soliton solutions obtained is depicted in some interesting simulations.