Some novel integration techniques to explore the conformable M-fractional Schrödinger-Hirota equation

Abstract

The current study deals with exact soliton solutions for Schrödinger-Hirota (SH) equation via two modified integration methods. Those methods are known as the improved (G′/G)-expansion method and the Kudryashov method. This model is a generalized version of the nonlinear Schrödinger (NLS) equation with higher order dispersion and cubic nonlinearity. It can be considered as a more accurate approximation than the NLS equation in explaining wave propagation in the ocean and optical fibers. A novel derivative operator named as the conformable truncated M-fractional is used to study the above mentioned model. The obtained results can be used in describing the Schrödinger-Hirota equation in some better way. Moreover the obtained results are verified through symbolic computational software. Also, the obtained results show that the suggested approaches have broaden capacity to secure some new soliton type solutions for the fractional differential equations in an effective way. In the end, the results are also explained through their graphical representations.