A robust fuzzy-fractional approach for the atmospheric internal wave model

The study of internal atmospheric waves, also known as gravity waves, which are detectable inside the fluid rather than at the fluid surface, is presented in this work. We have used the time-fractional and fuzzy-fractional techniques to solve the differential equation system representing the atmospheric internal waves model. The $q$-Homotopy analysis Shehu transform technique ($q$-HAShTM) is used to solve the model. The method helps find convergent solutions since it helps solve nonlinearity, and the fractional derivative can be easily computed using the Shehu transform. Finally, the obtained solution is compared for the particular case of $\alpha =1$ with the HAM solution to explain the method’s accuracy.