FDA Express

Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics.

Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes.

Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques

More information on this book can be found by the following link:

http://books.google.com.hk/books?id=_YFtAAAAQBAJ&dq=fractional+calculus&hl=zh-CN&sa=X&ei=XomGU5rEK8Tf8AXnwIGoBg&ved=0CFEQ6AEwCQ

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Diversity Fractional Differentiation for System Dynamics

Alain Oustaloup

Book Description

Based on a structured approach to diversity, notably inspired by various forms of diversity of natural origins, Diversity and Non-integer Derivation Applied to System Dynamics provides a study framework to the introduction of the non-integer derivative as a modeling tool. Modeling tools that highlight unsuspected dynamical performances (notably damping performances) in an "integer" approach of mechanics and automation are also included. Written to enable a two-tier reading, this is an essential resource for scientists, researchers, and industrial engineers interested in this subject area. Table of Contents:

1. From Diversity to Unexpected Dynamic Performance.

2. The Robustness of Damping.

3. Fractional Differentiation and its Memory.

4. CRONE Suspension Idea.

5. CRONE Control Idea

More information on this book can be found by the following link:

http://books.google.com.hk/books?id=yT7glgEACAAJ&dq=fractional+modeling&hl=zh-CN&sa=X&ei=W42GU7vDEYb58QW17oKYBg&ved=0CCIQ6AEwAA

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Journals

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Communications in Nonlinear Science and Numerical Simulation

Volume 19, Issue 10 (selected)

On the numerical computation of the Mittag-Leffler function

Duarte Valério, José Tenreiro Machado

Estimation of parameters in the fractional compound Poisson process

Ying Wang, Dehui Wang, Fukang Zhu

Asymptotic stability of a two-group stochastic SEIR model with infinite delays

Meng Liu, Chuanzhi Bai, Ke Wang

Coupled lattice Boltzmann method for simulating electrokinetic flows: A localized scheme for the Nernst–Plank model

Hiroaki Yoshida, Tomoyuki Kinjo, Hitoshi Washizu

Nonlinear Schrödinger equation containing the time-derivative of the probability density: A numerical study

Ji Luo

Power laws behavior in multi-state elastic models with different constraints in the statistical distribution of elements

M. Scalerandi, A.S. Gliozzi, S. Idjimarene

Principal resonance responses of SDOF systems with small fractional derivative damping under narrow-band random parametric excitation

Di Liu, Jing Li, Yong Xu

Fault detection based on fractional order models: Application to diagnosis of thermal systems

Asma Aribi, Christophe Farges, Mohamed Aoun, Pierre Melchior, Slaheddine Najar, Mohamed Naceur Abdelkrim

Steady-state, self-oscillating and chaotic behavior of a PID controlled nonlinear servomechanism by using Bogdanov–Takens and Andronov–Poincaré–Hopf bifurcations

Manuel Pérez-Molina, Manuel F. Pérez-Polo

Image encryption based on synchronization of fractional chaotic systems

Yong Xu, Hua Wang, Yongge Li, Bin Pei

Persistence and extinction of a stochastic non-autonomous Gilpin–Ayala system driven by Lévy noise

Qun Liu, Yanlai Liang

Synchronization of two coupled multimode oscillators with time-delayed feedback

Yulia P. Emelianova, Valeriy V. Emelyanov, Nikita M. Ryskin

Analytic study on a state observer synchronizing a class of linear fractional differential systems

Xian-Feng Zhou, Qun Huang, Wei Jiang, Song Liu

Dynamics of a driven magneto-martensitic ribbon

Ritupan Sarmah, G. Ananthakrishna

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Nonlinear dynamics

Volume 76, Issue 4

Hyperchaos synchronization of fractional-order arbitrary dimensional dynamical systems via modified sliding mode control

Ling Liu, Wen Ding, Chongxin Liu, Huigang Ji, Chuqing Cao

Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

Leipo Liu, Jiexin Pu, Xiaona Song, Zhumu Fu, Xiaohong Wang

Primary and secondary resonance analyses of clamped–clamped micro-beams

D. Younesian, M. Sadri, E. Esmailzadeh

Nonlinear vibrations of a single-walled carbon nanotube for delivering of nanoparticles

Keivan Kiani

Highly efficient nonlinear energy sink

Mohammad A. AL-Shudeifat

The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets

Yun Zeng, Lixiang Zhang, Yakun Guo, Jing Qian, Chenli Zhang

Types of coefficient constraints of coupled nonlinear Schrödinger equations for elastic and inelastic interactions between spatial solitons with symbolic computation

Wen-Jun Liu, Ming Lei

A new image alternate encryption algorithm based on chaotic map

Xingyuan Wang, Kang Guo

Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice

Jun Ma, Xinyi Wu, Runtong Chu, Liping Zhang

Bifurcation analysis of a nonlinear pendulum using recurrence and statistical methods: applications to fault diagnostics

C. A. Kitio Kwuimy, M. Samadani, C. Nataraj

Actuator fault diagnosis for uncertain T–S fuzzy systems with local nonlinear models

Huimin Wang, Dan Ye, Guang-Hong Yang

Algebraic analysis of a RGB image encryption algorithm based on DNA encoding and chaotic map

Akram Belazi, Houcemeddine Hermassi, Rhouma Rhouma, Safya Belghith

Postbuckling instability of nonlinear nanobeam with geometric imperfection embedded in elastic foundation

Hossein Mohammadi, Mojtaba Mahzoon, Mohsen Mohammadi…

A new car-following model with consideration of inter-vehicle communication

Tieqiao Tang, Weifang Shi, Huayan Shang, Yunpeng Wang

Nonlinear behavior analysis of geared rotor bearing system featuring confluence transmission

Haodong Gao, Yidu Zhang

Distributed proportional plus second-order spatial derivative control for distributed parameter systems subject to spatiotemporal uncertainties

Jun-Wei Wang, Han-Xiong Li, Huai-Ning Wu

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Paper Highlight
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Forced oscillations of a body attached to a viscoelastic rod of fractional derivative type

Teodor M. Atanackovic, Stevan Pilipovic, Dusan Zorica

Publication information: Teodor M. Atanackovic, Stevan Pilipovic, Dusan Zorica. Forced oscillations of a body attached to a viscoelastic rod of fractional derivative type. International Journal of Engineering Science, 2013, 64, 54–65.

http://www.sciencedirect.com/science/article/pii/S0020722513000037

Abstract

We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate a single function of complex variable that plays a key role in finding the solution of the system and in determining its properties. This function could be defined for a linear viscoelastic bodies of integer/fractional derivative type.

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Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications

Mohammed Al-Refai, Yuri Luchko

Publication information: Mohammed Al-Refai, Yuri Luchko. Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Fractional Calculus and Applied Analysis, 2014, 17 (2), 483-498.

http://link.springer.com/article/10.2478/s13540-014-0181-5

Abstract

In this paper, the initial-boundary-value problems for the one-dimensional linear and non-linear fractional diffusion equations with the Riemann-Liouville time-fractional derivative are analyzed. First, a weak and a strong maximum principles for solutions of the linear problems are derived. These principles are employed to show uniqueness of solutions of the initial-boundary-value problems for the non-linear fractional diffusion equations under some standard assumptions posed on the non-linear part of the equations. In the linear case and under some additional conditions, these solutions can be represented in form of the Fourier series with respect to the eigenfunctions of the corresponding Sturm-Liouville eigenvalue problems.

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The End of This Issue

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