### A fractional elasto-viscoplastic model for describing

Jun 30 2020 · In order to solve the analytical solution of the general rate-dependent model and make the theoretical model better reflect the creep behavior of soil the fractional calculus theory is applied to the EVP (elastic–viscoplastic) model based on the overstress theory. A fractional strain rate model is proposed to construct a constitutive equation of fractional strain rate.

Get Price### Applications of variable-order fractional operators a review

Variable-order fractional calculus (VO-FC) is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes. Recognizing this untapped potential the scientific community has been intensively exploring applications of VO-FC to the modelling of engineering and physical systems.

Get Price### FRActional CALculus MOdelling

Furthermore papers related to Fractional Calculus Modelling by promoters and/or their associates can be down-loaded. The WEB project has been presented on 7 December 2000 at the Free University of Berlin in the occasion of the Fest-colloquium in honour of Rudolf GORENFLO for his 70-th birthday.

Get Price### BIOLOGICALLY INSPIRED CONTROL AND MODELING OF

fractional calculus (FC). Key words biologically inspired systems control algorithms modeling fractional calculus stability 1. INTRODUCTION The field of biomimetics and biologically inspired principles from the application of methods and systems found in nature to

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Jul 09 2004 · Abstract We have developed a model using fractional calculus for the isochronal description of the relative complex permittivity taking into account three relaxation phenomena. The relaxation processes in organic dielectric materials (semi-crystalline polymers) are associated to molecular motions to a new structural equilibrium of less energy.

Get Price### Measuring memory with the order of fractional derivative

Dec 05 2013 · For example the fractional Maxwell model 12 is a one-stage model. As the combination of two simple models it has a more complicated expression than equation (1) .

Get Price### Fractional models and their applications

Nov 10 2011 · An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications. This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series

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Jul 09 2004 · Abstract We have developed a model using fractional calculus for the isochronal description of the relative complex permittivity taking into account three relaxation phenomena. The relaxation processes in organic dielectric materials (semi-crystalline polymers) are associated to molecular motions to a new structural equilibrium of less energy.

Get Price### (PDF) Fractional Calculus Models and Numerical Methods

The second edition of the book has been expanded and now includes a discussion of additional newly developed numerical methods for fractional calculus and a chapter on the application of

Get Price### Application of fractional calculus methods to viscoelastic

Results show that the application of the fractional derivatives to the viscoelastic constitutive model can effectively reduce the number of the required parameters while giving an accurate prediction of viscoelastic behaviours of solid propellants.

Get Price### Application of fractional calculus methods to viscoelastic

Results show that the application of the fractional derivatives to the viscoelastic constitutive model can effectively reduce the number of the required parameters while giving an accurate prediction of viscoelastic behaviours of solid propellants.

Get Price### Modeling of discrete fracmemristor and its application

Jan 22 2020 · Generally speaking fractional-order calculus can be used to better describe the systems with memory effect and it is widely used in different fields including quantum mechanics electromagnetic oscillations control and material mechanics. 14–19 14. H. Rudolf Applications of Fractional Calculus in Physics (World Scientific 2000). 15.

Get Price### Some Applications of Fractional Calculus in Engineering

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless the application of FC just emerged in the last two decades due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a

Get Price### Applications of Fractional CalculusHikari

the application of fractional calculus in physics continuum mechanics signal processing and electromagnetics. Here we state some of applications. 1. First one It may be important to point out that the ﬁrst application of fractional calculus was made by Abel() in the solution of an integral

Get Price### Applications of Fractional CalculusHikari

the application of fractional calculus in physics continuum mechanics signal processing and electromagnetics. Here we state some of applications. 1. First one It may be important to point out that the ﬁrst application of fractional calculus was made by Abel() in the solution of an integral

Get Price### Applications of Fractional CalculusHikari

the application of fractional calculus in physics continuum mechanics signal processing and electromagnetics. Here we state some of applications. 1. First one It may be important to point out that the ﬁrst application of fractional calculus was made by Abel() in the solution of an integral

Get Price### Fractional Plasticity Model for Coarse Aggregates

Fractional plasticity has been originally proposed for capturing the state-dependent nonassociated behaviour of sand with no use of state variables and additional plastic potentials. However for coarse aggregates significant particle breakage would occur which could influence the stress-strain behaviour of the material by shifting the critical state line in the

### Application of fractional calculus in modelling ballast

Feb 01 2017 · Application of fractional calculus in modelling ballast deformation under cyclic loading 1. Introduction. Ballast usually serves as an essential track construction layer to bear the load transmitted by 2. Fractional calculus. In traditional calculus the n th derivative or integral of a function

Get Price### Fractional Equations and ModelsTheory and Applications

Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems. Recent developments in the modeling of various physical chemical and biological systems have clearly shown that fractional calculus is not just an exotic mathematical theory as it might have once seemed.

Get Price### Generalized plasticity and the modelling of soil behaviour

Yifei Sun Changjie Zheng Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential Advances in Difference Equations 10.1186/s 2019 1 (2019).

Get Price### Fractional calculus and applicationsSlideShare

Aug 18 2015 · Fractional calculus is the study of dq dxq (f (x)) for arbitrary real or complex values of q. The term fractional is a misnomer. q need not necessarily be a fraction (rational number). If q > 0 we have a fractional derivative of order q. If q < 0 we have a fractional integral of order −q.

Get Price### Fractional Equations and ModelsTheory and Applications

Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems. Recent developments in the modeling of various physical chemical and biological systems have clearly shown that fractional calculus is not just an exotic mathematical theory as it might have once seemed.

Get Price### Generalized plasticity and the modelling of soil behaviour

Yifei Sun Changjie Zheng Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential Advances in Difference Equations 10.1186/s 2019 1 (2019).

Get Price### Application of fractional calculus to the modeling of

Jul 29 2005 · A model based on the concept of fractional calculus is proposed for the description of the relative complex permittivity (ε r = ε ′ r − iε ′ r where ε ′ r and ε ″ r are the real and imaginary parts of ε r) in polymeric materials.This model takes into account three dielectric relaxation phenomena.

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Applications of fractional calculus to epidemiological models. Epidemiological spreading does not only happen from person to neighbouring person but often over wide distances when infected but asymptomatic persons travel and carry infection to others over wide distances. Superdiffusion has been suggested to model such spreading in spatially

Get Price### Application of fractional calculus in modelling ballast

A constitutive model based on fractional calculus is an efficient tool for modelling long term deformation and therefore is incorporated into a constitutive model for predicting the geotechnical

Get Price### Application of fractional calculus methods to viscoelastic

Results show that the application of the fractional derivatives to the viscoelastic constitutive model can effectively reduce the number of the required parameters while giving an accurate prediction of viscoelastic behaviours of solid propellants.

Get Price### Application of fractional calculus to modelling of

Jul 09 2004 · Abstract We have developed a model using fractional calculus for the isochronal description of the relative complex permittivity taking into account three relaxation phenomena. The relaxation processes in organic dielectric materials (semi-crystalline polymers) are associated to molecular motions to a new structural equilibrium of less energy.

Get Price### Application of Fractional Calculus to Rainfall Streamflow

fractional relaxation model is overcome by application of the Laplace transform of the pulse rainfall hyetograph following Wang and Wu (1983). The model parameters are fitted using the genetic algorithm. The fractional order cascade equations are tested for classical rainfall-runoff modelling using a set of 22 events for the River Nenagh.

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