On the Fractional Order Model of Viscoelasticity

Adolfsson, Klas; Enelund, Mikael; Olsson, Peter

doi:10.1007/s11043-005-3442-1

Cited by 271 publications

(135 citation statements)

References 14 publications

Supporting

Mentioning

131

Contrasting

Unclassified

Order By: Relevance

“…4 The mean of displacement < x > versus noise intensity σ F for different orders of derivative q. The other system parameters, the initial conditions and the simulation time interval are as in Fig.…”

Section: The Model and Equations Of Motionmentioning

confidence: 99%

On simulation of a bistable system with fractional damping in the presence of stochastic coherence resonance

Litak

Borowiec

2014

Nonlinear Dyn

View full text Add to dashboard Cite

A bistable dynamical system with the Duffing potential, fractional damping, and random excitation has been modelled. To excite the system, we used a stochastic force defined by Wiener random process of Gaussian distribution. As expected, stochastic resonance appeared for sufficiently high noise intensity. We estimated the critical value of the noise level as a function of derivative order q. For smaller order q, damping enhancement was reported.

show abstract

Section: The Model and Equations Of Motionmentioning

confidence: 99%

On simulation of a bistable system with fractional damping in the presence of stochastic coherence resonance

Litak

Borowiec

2014

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…On the other hand, higher order fractional differential equations have applications such as the fractional order elastic beam equations see [23], the fractional order viscoelastic material model see [24], the fractional viscoelastic model see [25][26][27] and so on. There has been no papers concerned with the solvability of boundary value problems for higher order impulsive fractional differential equations since it is difficult to convert an impulsive fractional differential equation to an equivalent integral equation.…”

Section: Introductionmentioning

confidence: 99%

Solvability of impulsive $$(n,n-p)$$ ( n , n - p ) boundary value problems for higher order fractional differential equations

Liu

2016

Math Sci

View full text Add to dashboard Cite

We present a new general method for converting an impulsive fractional differential equation to an equivalent integral equation. Using this method and employing a fixed point theorem in Banach space, we establish existence results of solutions for a boundary value problem of impulsive singular higher order fractional differential equation. An example is presented to illustrate the efficiency of the results obtained. A conclusion section is given at the end of the paper.

show abstract

“…Of all applications in biology, linear viscoelasticity is certainly the most popular field, for their ability to model hereditary phenomena with long memory (Berg (2009) ). Viscoelasticity has been shown to be the origin of the appearance of FO models in polymers (from the Greek: poly -many and meros -parts) (Adolfsson et al (2005)) and resembling biological tissues (Doehring et al (2005); Suki et al (1994)). …”

Section: Introductionmentioning

confidence: 99%

A fractional order impedance model to capture the structural changes in lungs

Ionescu

Copot

Keyser

2014

IFAC Proceedings Volumes

View full text Add to dashboard Cite

Robain.DeKeyser} @ UGent.be).Abstract: This paper introduces a correlation analysis between the structural changes occurring in the lungs and the corresponding variations in the fractional order value of an impedance model. It was discussed how variations in the wall thickness, cross-sectional area and elastic moduli in distal airways involved in respiratory process affect changes in the fractional order value. Two lumped models were discussed: i) a theoretical model derived from morphological information and ii) a lumped parametric model. Results indicate that a correlation analysis is possible for various degrees of obstruction and effects may be directly related to the identified fractional order value.

show abstract

On the Fractional Order Model of Viscoelasticity

Cited by 271 publications

References 14 publications

On simulation of a bistable system with fractional damping in the presence of stochastic coherence resonance

On simulation of a bistable system with fractional damping in the presence of stochastic coherence resonance

Solvability of impulsive $$(n,n-p)$$ ( n , n - p ) boundary value problems for higher order fractional differential equations

A fractional order impedance model to capture the structural changes in lungs

Contact Info

Product

Resources

About