一类分数阶非线性振子方程的特性研究

Study on properties of fractional nonlinear oscillator equations

将分数阶微分算子引入到黏弹性介质中的阻尼振动中建立分数阶非线性振动方程。利用Adomian分解方法借助Mathematica软件的符号计算功能求解了该类分数阶阻尼振动方程的近似解,研究了振子运动与方程中分数阶导数的关系。

In this paper, fractional calculus is introduced to describe the damping oscillator in viscoelastic material and the fractional nonlinear oscillator equation is established in this paper. Approximate solutions of the fractional equation are obtained using the Adomian decomposition method and with the aid of the symbolic computational system Mathematica. And the relationship between oscillator movement and fractional derivative is also studied.