Abstract
In this article, we will consider algebraic gravity solitary waves of the baroclinic atmosphere. The Benjamin-Ono (BO) equation will be obtained by employing multi-scale analysis and perturbation method. Based on the semi-inverse method and the Agrawal’s method, the time-fractional BO equation will be derived to describe the algebraic gravity solitary waves. We need to emphasis that the time-fractional differential-integral equation(time-fractional BO equation) is great different from the existing fractional order differential equation. Further, the conservation laws of the time-fractional BO equation will also be discussed. Finally, we will use the Hirota bidglinear method to find the exact multi-soliton solutions to the above equation and research the interaction between the soliton solutions. The results show that the propagation processes and characteristics of algebraic gravity solitary waves change with the change of the fractional order. Therefore, constructing time-fractional BO equation is not only of great theoretical value but also of more practical value for the study of algebraic gravity solitary waves of actual ocean and atmosphere.
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