Fractional oscillators can effectively deal with noise in the vibration. This paper adopts He's fractional derivative, which is defined through the variational iteration algorithm. Ji-Huan He's amplitude-frequency formulation is used to solve the fractional Duffing equation.

An anisotropic wave in a porous medium is a hot topic in the coastal protection. A fractal derivative model is established, and a variational principle is established for the anisotropic wave traveling. The variational principle reveals an energy conservation law during the traveling process.

The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffler functions of matric argument. The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1, the result here is simplified to that of first order differential equation.

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Abstract-The economic growth rate of China has gradually present a downward trend after 30 years sustained high-speed growth. Therefore, the improvement of economic efficiency and the optimization of industrial structure is a necessary requirement for sustainable development of China's economy. This paper not only analyzes the shortcomings of traditional DEA method applied in the industrial structure adjustment, but also proposes a new approach and model. Finally, we analyze the effectiveness of economic growth and give some information on industrial structure adjustment in Tianjin in the past 27 years.