汇报标题 (Title)：Analytical solution of fractional oscillation equation with two Caputo fractional derivatives
（含两个 Caputo分数阶导数的分数阶震荡方程的解析解）
汇报人 (Speaker)：段俊生 教授（上海利用技术大学）
汇报功夫 (Time)：2025年6月11日（周三）10:30-12:30
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
汇报提要：Analytical solution of initial value problem for the fractional oscillation equation with two Caputo fractional derivatives is investigated by using the Laplace transform and complex inverse integral method on the principal Riemann surface. It is proved by using the argument principle that the characteristic equation has a pair of conjugated simple complex roots with a negative real part on the principal Riemann surface. Then three fundamental solutions, the unit impulse response, the unit initial displacement response, and the unit initial rate response, are derived analytically. Each of these solutions is expressed into a superposition of a classical damped oscillation decaying exponentially and a real Laplace integration decaying in a negative power law. Finally, the asymptotic behaviors of these analytical solutions are determined as monotonous decays in a power of negative exponent.
