The Mixed Boundary Value Problems and Chebyshev Collocation Method for Caputo-Type Fractional Ordinary Differential Equations

Article Mathematics, Interdisciplinary Applications

Comparison of Two Different Analytical Forms of Response for Fractional Oscillation Equation

Jun-Sheng Duan et al.

Summary: The impulse response of the fractional oscillation equation was investigated using two different methods to obtain two different analytical forms, with detailed results in terms of analytic approximation and infinite integrals.

FRACTAL AND FRACTIONAL (2021)

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Article Mathematics, Interdisciplinary Applications

Vibration Systems with Fractional-Order and Distributed-Order Derivatives Characterizing Viscoinertia

Jun-Sheng Duan et al.

Summary: The paragraph discusses the characteristics and features of forced harmonic vibration systems with Liouville-Weyl fractional derivatives and distributed-order derivatives, including their impact on system viscosity, inertia, damping, and mass, as well as the derivation and analysis of equivalent integer-order vibration systems. By comparing frequency-amplitude curves and frequency-phase curves of the two vibration models, it is found that the distributed-order vibration model is more general and flexible than the fractional vibration system.

FRACTAL AND FRACTIONAL (2021)

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Article Mathematics, Interdisciplinary Applications

Simultaneous Characterization of Relaxation, Creep, Dissipation, and Hysteresis by Fractional-Order Constitutive Models

Jun-Sheng Duan et al.

Summary: By considering a six-parameter fractional constitutive model and its particular cases, this study focused on analyzing relaxation, creep, dissipation, and hysteresis phenomena. It was found that fractional constitutive models could effectively characterize the properties of viscoelastic bodies, with fractional orders alpha and beta being able to model real-world physical properties accurately.

FRACTAL AND FRACTIONAL (2021)

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Article Mechanics

The periodic response of a fractional oscillator with a spring-pot and an inerter-pot

Yu Li et al.

Summary: The study focuses on a fractional oscillation system with two Weyl-type fractional derivative terms, investigating the impact of fractional parameters on inertia, stiffness, and damping. The system's harmonic response, amplitude-frequency, and phase-frequency characteristics were deduced, while the steady-state response to general periodic excitation was obtained through Fourier series and superposition principle. The results show the applicability of the Weyl fractional operator in researching steady-state problems and the capability of fractional derivative in describing viscoelasticity and viscous inertia properties.

JOURNAL OF MECHANICS (2021)

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Article Computer Science, Interdisciplinary Applications