Journal ArticleDOI
Damping characteristics of a fractional oscillator
TLDR
In this article, a study of sinusoidally forced oscillations of a fractional oscillator was conducted, and it was shown that the system exhibits a rich variety of damping characteristics, which do not find any parallel in the damped harmonic oscillator system.Abstract:
A study of sinusoidally forced oscillations of a fractional oscillator shows that the system exhibits a rich variety of damping characteristics. While some aspects of the damping mimic the characteristic features of a damped harmonic oscillator, there are others, which do not find any parallel in the damped harmonic oscillator system. It is clearly demonstrated that the “free” and “forced” oscillations of a fractional oscillator are characterized by different damping parameters. While both depend on the fractional index α , the “free” oscillation damping depends on the “natural frequency”, ω 0 , of the oscillator, the “forced” oscillation damping depends in addition, on the “driving frequency”, ω . Furthermore, there is a different power-law tail associated with each of these cases.read more
Citations
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Journal ArticleDOI
Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results
TL;DR: In this article, the authors present the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics.
Journal ArticleDOI
The -Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey
TL;DR: In this article, the authors survey the properties of a transcendental function of the Wright type, nowadays known as 𝑀-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we generally refer to as time-fractional diffusion processes.
Journal ArticleDOI
Long-range cohesive interactions of non-local continuum faced by fractional calculus
TL;DR: In this paper, a non-local continuum model including long-range forces between non-adjacent volume elements has been studied, and the proposed model has been obtained as limit case of two fully equivalent mechanical models: (i) a volume element model including contact forces between adjacent volumes as well as distance decaying, between nonadjacent elements.
Journal ArticleDOI
Review of Some Promising Fractional Physical Models
TL;DR: Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, powerlaw long-term memory or fractal properties by using integrations and differentiation of noninteger orders.
Journal ArticleDOI
Review of Some Promising Fractional Physical Models
TL;DR: Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, non-local memory or fractal properties by using integrations and differentiation of non-integer orders as mentioned in this paper.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
BookDOI
Fractals and fractional calculus in continuum mechanics
TL;DR: Panagiotopoulos, O.K.Carpinteri, B. Chiaia, R. Gorenflo, F. Mainardi, and R. Lenormand as mentioned in this paper.
Book
Classical dynamics of particles and systems
Jerry B. Marion,J. Gillis +1 more
TL;DR: In this paper, the Calculus of Variation is used to describe the dynamics of a system of Particles and their motion in a noninertial reference frame, including central-force motion and coupling oscillations.