Some new types of optical solitons to the time-fractional new hamiltonian amplitude equation via extended Sinh-Gorden equation expansion method

Abstract

This research is about some new exact solitons to the new Hamiltonian amplitude equation with novel truncated M-fractional derivatives. Extended Sinh-Gordon equation expansion method (ShGEEM) is applied to obtain solitons to the new Hamiltonian amplitude equation with novel truncated M-fractional derivatives. The obtained results may be used in the description of the model in a fruitful way. The novel derivative operator is applied to study the aforementioned model. The achieved results are in the form of dark, bright, and combo optical solitons. The achieved solutions are also verified by using the Mathematica software. Some of the solutions are drawn in two and three dimensions so that the results can be easily discussed through them.