4 papers
Equivalence of the Initialized Riemann-Liouville Derivatives and the Initialized Caputo Derivatives
Jian Yuan, Guozhong Xiu, Bao Shi
Initialization of fractional differential equations remains an ongoing problem. In recent years, the initialization function approach and the infinite state approach provide two ef…
Hereditary effects of exponentially damped oscillators with past histories
Jian Yuan, Guozhong Xiu, Bao Shi +1
Hereditary effects of exponentially damped oscillators with past histories are considered in this paper. Nonviscously damped oscillators involve hereditary damping forces which dep…
Sliding control for single-degree-of-freedom fractional oscillators
Jian Yuan, Bao Shi, Guozhong Xiu
This paper proposes fractional sliding control designs for single-degree-of-freedom fractional oscillators respectively of the Kelvin-Voigt type, the modified Kelvin-Voigt type and…
Mechanical energy and mean equivalent viscous damping for SDOF fractional oscillators
Jian Yuan, Bao Shi, Mingjiu Gai +1
This paper addresses the total mechanical energy of a single degree of freedom fractional oscillator. Based on the energy storage and dissipation properties of the Caputo fractiona…