Fractional Calculus In Oscillator Applications

Fractional Calculus (FC) is one newly-developed mathematical branch. It comes forth due to many observed physical or mathematical problems beyond the understanding of theorists under the use of previous theory. FC is currently being considered the most proper mathematical tool to connect the mathematical theory with the real world. It has been widely used in Physics, Biology, Medicine and Society etc. and great success has been gained already.In the first chapter, this thesis analyzes the origin and development of FC as well as its fundamental theory.In the second chapter, this thesis summarizes several applications of FC on Oscillator. Then we can know that the modification by FC brings forth new properties, such as change of energy, new character of speed and the change of amplitude.In the last chapter, the thesis summarizes the newly-developed definition of speed and acceleration (respectively represented by v_f, a_f).Then this thesis uses the speed function to time t to form the oscillating dynamic equation. The solution is obtained and its approximate form is analyzed. The fractional acceleration is gained from the solution and analyzed also. In the last, the thesis unifies the inner friction and outer friction in the dynamic equation with one fractional variableγ. The final...