Ali, MohammedAlquran, MarwanJaradat, ImadAbu Afouna, NourBaleanu, Dumitru2021-02-102021-02-102020Ali, Mohammed ...et al. (2020). "DYNAMICS OF INTEGER-FRACTIONAL TIME-DERIVATIVE FOR THE NEW TWO-MODE KURAMOTO-SIVASHINSKY MODEL", Romanian Reports in Physics, Vol. 72, No. 1.1221-14511841-8759http://hdl.handle.net/20.500.12416/4578In this paper, we investigate the dynamics of a nonlinear model responsible for the transition of turbulence phenomena and cellular instabilities to a chaos. The two-mode Kuramoto-Sivashinsky (TMKS) model is an example of such application. We study both integer and fractional time-derivative involved in this model. Solitary wave solutions and approximate analytical solutions will be derived to TMKS model by means of well-posed different techniques. The mechanism of the concepts of two-mode and time-fractional derivative will be discussed in this work. Finally, both 2-dimensional and 3-dimensional plots will be provided to support our findings.eninfo:eu-repo/semantics/closedAccessTwo-Mode Kuramoto-Sivashinsky (TMKS) ModelKudryashov-Expansion MethodTime-Fractional TMKSMaclaurin SeriesArticle721