The fundamental objective of this paper is to study the effectiveness of magnetic field and gravity on an isotropic homogeneous thermoelastic structure based on four theories of generalized thermoelasticity. In another meaning, the models of coupled dynamic theory (CDT), Lord-Shulman (LS), Green-Lindsay (GL) as well as Green-Naghdi (GN II) will be taken in the consideration. Then, applying the harmonic method (normal mode technique), the solution of the governing equations and the expressions for the components of the displacement, temperature and (Mechanical and Maxwell's) stresses is taken into account and calculated numerically. The impacts of the gravity and magnetic field are illustrated graphically which are pronounced on the different physical quantities. Finally, the results of some research that others have previously obtained may be found some or all of them as special cases from this study.
In this paper, the generalized dissipative Kawahara equation in the sense of conformable fractional derivative is presented and solved by applying the tanh-coth-expansion and sine-cosine function techniques. The quadratic-case and cubic-case are investigated for the proposed model. Expected solutions are obtained with highlighting to the effect of the presence of the alternative fractional-derivative and the effect of the added dissipation term to the generalized Kawahara equation. Some graphical analysis is presented to support the findings of the paper. Finally, we believe that the obtained results in this work will be important and valuable in nonlinear sciences and ocean engineering.

