FDA Express

Contrary to most books on fractional calculus which start with definitions of fractional derivatives in terms of integrals, here one uses a definition expressed as the limit of fractional difference, what allows us to expand the theory step by step exactly like with Leibniz calculus, by handling infinitely small increments. It follows that the physical significance of this calculus sticks to real problems and that, as a result, it is quite suitable (perhaps excellent) in systems modeling. Physical increments have a parlance in modeling which one can find in our fractional calculus, but is nowhere in the definition of fractional derivative via integrals. Last but not least, the book deals with non-differentiable functions, whilst most classical approaches to fractional calculus refer to the Caputo definition which deals with differentiable functions.

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

http://www.powells.com/biblio/9789814440035

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Anomalous Diffusion: From Basics to Applications

Andrzej Pekalski, Katarzyna Sznajd-Weron

Book Description

This collection of articles gives a nice overview of the fast growing field of diffusion and transport. The area of non-Browman statistical mechanics has many extensions into other fields like biology, ecology, geophysics etc. These tutorial lectures address e.g. Lévy flights and walks, diffusion on metal surfaces or in superconductors, classical diffusion, biased and anomalous diffusion, chemical reaction diffusion, aging in glassy systems, diffusion in soft matter and in nonsymmetric potentials, and also new problems like diffusive processes in econophysics and in biology.

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

http://link.springer.com/book/10.1007/BFb0106828

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An Introduction to Fractional Control

Duarte Valerio, José Sá da Costa

Book Description

An Introduction to Fractional Control outlines the theory, techniques and applications of fractional control. The theoretical background covers fractional calculus with real, complex and variable orders, fractional transfer functions, fractional identification and pseudostatespace representations, while the control systems explored include: fractional lead control, fractional lag control, first, second and third generation Crone control, fractional PID, PI and PD control, fractional sliding mode control, logarithmic phase Crone control, fractional reset control, fractional H2 and H8 control, fractional predictive control, trajectory planning and fractional timevarying control. Each chapter contains solved examples, where the subject addressed is either expanded or applied to concrete cases, and references for further reading. Common definitions and proofs are included, along with a bibliography, and a discussion of how MATLAB can be used to assist in the design and implementation of fractional control. This is an essential guide for researchers and advanced students of control engineering in academia and industry.

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

http://www.theiet.org/resources/books/control/aitfc.cfm

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Journals

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Computers & Mathematics with Applications

Volume 67, Issue 8-9 (selected)

A class of nonlocal tensor telegraph-diffusion equations applied to coherence enhancement

Wei Zhang, Jiaojie Li, Yupu Yang

Efficient Kansa-type MFS algorithm for time-fractional inverse diffusion problems

Liang Yan, Fenglian Yang

The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations

Na Huang, Changfeng Ma

A fast multiphase image segmentation model for gray images

Yunyun Yang, Yi Zhao, Boying Wu, Hongpeng Wang

Hyperbolic conservation laws for continuous two-phase flow without mass exchange

Francisco J. Collado

Complex nonlinear parameter estimation (CNPE) and obstacle shape reconstruction

Ju-Hyun Lee, Sungkwon Kang

Efficient preconditioner updates for unsymmetric shifted linear systems

Wei-Hua Luo, Ting-Zhu Huang, Liang Li, Yong Zhang, Xian-Ming Gu

Computing real low-rank solutions of Sylvester equations by the factored ADI method

Peter Benner, Patrick Kürschner

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

S. Chen, F. Liu, K. Burrage

Adaptively weighted numerical integration over arbitrary domains

Vaidyanathan Thiagarajan, Vadim Shapiro

A parallel deterministic solver for the Schrödinger–Poisson–Boltzmann system in ultra-short DG-MOSFETs: Comparison with Monte-Carlo

Francesco Vecil, José M. Mantas, María J. Cáceres, Carlos Sampedro, Andrés Godoy, Francisco Gámiz

An isogeometric analysis for elliptic homogenization problems

H. Nguyen-Xuan, T. Hoang, V.P. Nguyen

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Nonlinear dynamics

Volume 76, Issue 2-3 (selected)

Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method

M. Srivastava, S. P. Ansari, S. K. Agrawal, S. Das, A. Y. T. Leung

Nonlinear control for teleoperation systems with time varying delay

S. Islam, P. X. Liu, A. El Saddik

Robust adaptive synchronization for a class of chaotic systems with actuator failures and nonlinear uncertainty

Dan Ye, Xingang Zhao

Dynamics of microscopic objects in optical tweezers: experimental determination of underdamped regime and numerical simulation using multiscale analysis

Mahdi Haghshenas-Jaryani, Bryan Black, Sarvenaz Ghaffari, James Drake…

Optimal bounded control of quasi-nonintegrable Hamiltonian systems using stochastic maximum principle

X. D. Gu, W. Q. Zhu

Regular oscillations, chaos, and multistability in a system of two coupled van der Pol oscillators: numerical and experimental studies

J. Kengne, J. C. Chedjou, M. Kom, K. Kyamakya, V. Kamdoum Tamba

Finite-time tracking control for a class of high-order nonlinear systems and its applications

Yingying Cheng, Haibo Du, Yigang He, Ruting Jia

Breaking an image encryption algorithm based on hyper-chaotic system with only one round diffusion process

Yushu Zhang, Di Xiao, Wenying Wen, Ming Li

Spatiotemporal solitons on cnoidal wave backgrounds in three media with different distributed transverse diffraction and dispersion

Hai-Ping Zhu

Robust synchronization of two different uncertain fractional-order chaotic systems via adaptive sliding mode control

Longge Zhang, Yan Yan

Effect of parameter mismatch and time delay interaction on density-induced amplitude death in coupled nonlinear oscillators

Amit Sharma, K. Suresh, K. Thamilmaran, Awadhesh Prasad…

Segmented inner composition alignment to detect coupling of different subsystems

Jing Wang, Pengjian Shang, Aijin Lin, Yuechen Chen

Use of independent rotation field in the large displacement analysis of beams

Jieyu Ding, Michael Wallin, Cheng Wei, Antonio M. Recuero…

Decentralized adaptive neural network control for mechanical systems with dead-zone input

Chang-Chun Hua, Yan-Fei Chang

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Paper Highlight
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Some properties of the fundamental solution to the signalling problem for the fractional diffusion-wave equation

Yuri Luchko, Francesco Mainardi

Publication information: Yuri Luchko, Francesco Mainardi, Some properties of the fundamental solution to the signalling problem for the fractional diffusion-wave equation, Central European Journal of Physics, 2013, 11(6), 666-675. http://link.springer.com/article/10.2478/s11534-013-0247-8

Abstract

In this paper, the one-dimensional time-fractional diffusion-wave equation with the Caputo fractional derivative of order α, 1 ≤ α ≤ 2 and with constant coefficients is revisited. It is known that the diffusion and the wave equations behave quite differently regarding their response to a localized disturbance. Whereas the diffusion equation describes a process where a disturbance spreads infinitely fast, the propagation speed of the disturbance is a constant for the wave equation. We show that the time-fractional diffusion-wave equation interpolates between these two different responses and investigate the behavior of its fundamental solution for the signalling problem in detail. In particular, the maximum location, the maximum value, and the propagation velocity of the maximum point of the fundamental solution for the signalling problem are described analytically and calculated numerically.

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Solution set for fractional differential equations with Riemann-Liouville derivative

Yurilev Chalco-Cano, Juan J. Nieto, Abdelghani Ouahab, Heriberto Román-Flores

Publication information: Yurilev Chalco-Cano, Juan J. Nieto, Abdelghani Ouahab, Heriberto Román-Flores, Solution set for fractional differential equations with Riemann-Liouville derivative. Fractional Calculus and Applied Analysis, 2013,16(3), 682-694. http://link.springer.com/article/10.2478/s13540-013-0043-6

Abstract

We study an initial value problem for a fractional differential equation using the Riemann-Liouville fractional derivative. We obtain some topological properties of the solution set: It is the intersection of a decreasing sequence of compact nonempty contractible spaces. We extend the classical Kneser’s theorem on the structure solution set for ordinary differential equations.

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The End of This Issue

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