Extracting the exact solitons of time-fractional three coupled nonlinear Maccari’s system with complex form via four different methods

Abstract

This current research is considered some new exact soliton solutions to the time-fractional three coupled non-linear Maccari’s system in complex form with novel truncated M-fractional derivative. The obtained results may be used in the description of the model in fruitful way. The novel derivative operator is applied to study the aforementioned model. In addition, the achieved results are included in the form of dark, bright and combo optical solitons. The achieved solutions are also verified by using the MATHEMATICA software. Modified integration methods, namely, the Kudryashov method, the Expafunction method, the extended (G′/G)−expansion method and the extended ShGEEM are applied to achieve the results. Obtained solutions are remodeled in several hyperbolic and trigonometric forms based on different restrictions between parameters involved in equations and integration constants that appear in the solutions. A few significant ones among the reported solutions are pictured to perceive the physical utility and peculiarity of the considered model using mathematical software. These optical solitons suggest that these three methods are useful, easy to use and effective than other methods.

Keywords

• Three coupled non-linear Maccari’s system
• Truncated M-fractional derivative
• Kudryashov method
• Expa function method
• Extended (G′/G)–expansion method
• Extended shGEEM