M-Fractional soliton solutions of fifth order generalized nonlinear fractional differential equation via (G′/G 2 )-expansion method

Abstract

Abstract The motivation of this research is to investigate four fifth order generalized nonlinear fractional differential equations. Here, we analyze a local derivative, as conformable sense called truncated M-fractional derivative. We also discuss some properties satisfied by the derivative. An effective analytical method namely ( G ′ / G 2 ) -expansion method combined with truncated M-fractional derivative will be studied. As a result, the different types of new soliton solutions were obtained such as dark soliton, bright soliton, kink soliton and periodic soliton wave solutions etc and are verified through MATHEMATICA. This approach is a strong contender for future use in resolving the other problems of a similar nature. A visualization of a few findings is given, which demonstrates the effectiveness and suitability of the suggested approach in producing solutions with well-understood physical behavior. The above mentioned method is more reliable and efficient and simple as compared to rest of the methods to solve the fifth order generalized nonlinear fractional differential equations. The results will also be displayed in two dimensional as well as in three dimensional plots.