# application of fractional calculus in modelling ballast

### 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. 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### 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. 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### Fractional Calculus in the Mathematical Modelling

The use of fractional derivatives for the mathematical modelling of viscoelastic materials is quite natural ˙(t)stress "(t)strain (at time t) Constitutive equations give the relation between ˙and ". Fractional calculus provides novel mathematical tools for modeling physical and biological processes. The bioheat equation is often used as a first order model of heat transfer in biological systems. In this paper we describe formulation of bioheat transfer in one dimension in terms of fractional order differentiation with respect to time.

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. 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### 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). 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### 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

### Yifei SUN Humboldt Fellow PhD MSc BSc(Hons) Ruhr

Application of fractional calculus in modelling ballast deformation under cyclic loading for geotechnical applications. The original fractional plasticity is reformulated in this study by 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### 1706.06446 The Concepts and Applications of Fractional

Jun 20 2017 · Recently researchers have been applying fractional calculus in order for probing viscoelasticity of such materials with a high precision. Fractional calculus is a powerful tool for modeling complex phenomenon. In this tutorial based paper we try present clear descriptions of the fractional calculus its techniques and its implementation. This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models.

Get Price### Advanced Topics on Applications of Fractional Calculus on

The next three Chapters (5 6 7) are related to applications of fractional calculus in bio-engineering fields. Chapter 5 is dedicated to the mathematical modeling of skin structure applying fractional calculus where it is proposed the skin structure as a more complex system consisting of several layers which describes series 34 Application of fractional calculus in modelling ballast 35 deformation under cyclic loading 36 37 ABSTRACT Most constitutive models can only simulate cumulative deformation after a 38 limited number of cycles. However railroad ballast usually experiences a large number of 39 train passages that cause history-dependent long-term deformation. . Fractional calculus i

Get Price### Development of Fractional Trigonometry and an

Almusharrf Amera "Development of Fractional Trigonometry and an Application of Fractional Calculus to Pharmacokinetic Model" (2011).Masters Theses Specialist Projects.Paper 1048. application of fractional calculus to pharmacokinetic model which is used to study the drug concentration in the body. CHAPTER 1 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.

Get Price### Effect of integrating memory on the performance of the

May 23 2018 · A fractional plasticity model for geomaterials is proposed by using the fractional derivative. Due to the integral definition of the fractional derivative the range of load memory for calculating the flow direction may influence the subsequent model performance. Therefore an investigation on the memory dependence of the model was conducted. 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### Fractional calculusWikipedia

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D = () and of the integration operator J = ∫ () and developing a calculus for such operators generalizing the classical one.. In this context the term powers refers to iterative application of a 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### Fractional Calculus in the Mathematical Modelling

The use of fractional derivatives for the mathematical modelling of viscoelastic materials is quite natural ˙(t)stress "(t)strain (at time t) Constitutive equations give the relation between ˙and ". 4. Modeling of speech signals using fractional calculus In this paper a novel approach for speech signal modeling using fractional calculus is presented. This approach is contrasted with the celebrated Linear Predictive Coding (LPC) approach which is based on integer order models. It is demonstrated via numerical simulations that by using a few

Get Price### Application of fractional calculus in modeling and solving

Application of fractional calculus in modeling and solving the bioheat equation R. Magin1 Y. Sagher2 S. Boregowda1 3 1Department of Bioengineering University of Illinois at Chicago USA 2Department of Mathematical Sciences Florida Atlantic University USA 3University of Chicago Graduate School of Business USA Abstract Fractional calculus provides novel mathematical tools for modeling Most constitutive models can only simulate cumulative deformation after a limited number of cycles. However railroad ballast usually experiences a large number of train passages that cause history-dependent long-term deformation. Fractional calculus is an efficient tool for modelling this phenomenon and therefore is incorporated into a constitutive model for predicting the cumulative

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 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### 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. The use of fractional derivatives for the mathematical modelling of viscoelastic materials is quite natural ˙(t)stress "(t)strain (at time t) Constitutive equations give the relation between ˙and ".

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 Application of fractional calculus in modelling ballast deformation under cyclic loading for geotechnical applications. The original fractional plasticity is reformulated in this study by

Get Price### Applications of fractional calculus to epidemiological models

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 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.

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