FDA Express

This book provides an overview of the research done and results obtained during the last ten years in the fields of fractional systems control, fractional PI and PID control, robust and CRONE control, and fractional path planning and path tracking. Coverage features theoretical results, applications and exercises.

The book will be useful for post-graduate students who are looking to learn more on fractional systems and control. In addition, it will also appeal to researchers from other fields interested in increasing their knowledge in this area.

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

http://www.springer.com/us/book/9789401798068

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Linear Fractional Diffusion-Wave Equation for Scientists and Engineers

Povstenko, Yuriy

Book Description

This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates.

The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences.

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

http://www.springer.com/us/book/9783319179537

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Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols

Umarov, Sabir

Book Description

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.

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

http://www.springer.com/us/book/9783319207704

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Journals

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European Journal of Mechanics - A/Solids

(Selected)

Fractional Euler–Bernoulli beams: Theory, numerical study and experimental validation

W. Sumelka, T. Blaszczyk, C. Liebold

Well-posedness of an integro-differential equation with positive type kernels modeling fractional order viscoelasticity

Fardin Saedpanah

Fractional time-dependent deformation component models for characterizing viscoelastic Poisson's ratio

Deshun Yin, Xiaomeng Duan, Xuanji Zhou

Fractional order generalized electro-magneto-thermo-elasticity

Ya Jun Yu, Xiao Geng Tian, Tian Jian Lu

Theory of fractional order in electro-thermoelasticity

Magdy A. Ezzat, Ahmed S. El Karamany

Size-dependent generalized thermoelasticity using Eringen's nonlocal model

Y. Jun Yu, Xiao-Geng Tian, Xin-Rang Liu

3D analyses of the global stability loss of the circular hollow cylinder made from viscoelastic composite material

S.D. Akbarov, S. Karakaya

Nonlocal longitudinal vibration of viscoelastic coupled double-nanorod systems

Danilo Karličić, Milan Cajić, T. Murmu, S. Adhikari

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Control Engineering Practice

(selected)

LPV continuous fractional modeling applied to ultracapacitor impedance identification

Jean-Denis Gabano, Thierry Poinot, Houcem Kanoun

Nonlinear thermal system identification using fractional Volterra series

Asma Maachou, Rachid Malti, Pierre Melchior, Jean-Luc Battaglia, Alain Oustaloup, Bruno Hay

Fractional-order filters for active damping in a lithographic tool

Hans Butler, Corné de Hoon

Fractional order robust control for cogging effect compensation in PMSM position servo systems: Stability analysis and experiments

Ying Luo, YangQuan Chen, Hyo-Sung Ahn, YouGuo Pi

Roll-channel fractional order controller design for a small fixed-wing unmanned aerial vehicle

Haiyang Chao, Ying Luo, Long Di, Yang Quan Chen

Design of a fractional order PID controller for an AVR using particle swarm optimization

Majid Zamani, Masoud Karimi-Ghartemani, Nasser Sadati, Mostafa Parniani

Tuning and auto-tuning of fractional order controllers for industry applications

Concepción A. Monje, Blas M. Vinagre, Vicente Feliu, YangQuan Chen

Fractional robust control of main irrigation canals with variable dynamic parameters

V. Feliu-Batlle, R. Rivas Pérez, L. Sánchez Rodríguez

An improved linear fractional model for robustness analysis of a winding system

Edouard Laroche, Dominique Knittel

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Paper Highlight
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A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators

Boyuan Jin, Jinhui Yuan, Kuiru Wang, Xinzhu Sang, Binbin Yan, Qiang Wu, Feng Li, Xian Zhou, Guiyao Zhou, Chongxiu Yu, Chao Lu, Hwa Yaw Tam & P. K. A. Wai.

Publication information: Jin, B. et al. A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators. Scientific Reports 5, 14216; doi: 10.1038/srep14216 (2015).

http://www.nature.com/articles/srep14216

Abstract

Microring-based photonic fractional differentiators play an important role in the on-chip all-optical signal processing. Unfortunately, the previous works do not consider the time-reversal and the time delay characteristics of the microring-based fractional differentiator. They also do not include the effect of input pulse width on the output. In particular, it cannot explain why the microring-based differentiator with the differentiation order n > 1 has larger output deviation than that with n < 1, and why the microring-based differentiator cannot reproduce the three-peak output waveform of an ideal differentiator with n > 1. In this paper, a comprehensive theoretical model is proposed. The critically-coupled microring resonator is modeled as an ideal first-order differentiator, while the under-coupled and over-coupled resonators are modeled as the time-reversed ideal fractional differentiators. Traditionally, the over-coupled microring resonators are used to form the differentiators with 1 < n < 2. However, we demonstrate that smaller fitting error can be obtained if the over-coupled microring resonator is fitted by an ideal differentiator with n < 1. The time delay of the differentiator is also considered. Finally, the influences of some key factors on the output waveform and deviation are discussed. The proposed theoretical model is beneficial for the design and application of the microring-based fractional differentiators.

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Measuring memory with the order of fractional derivative

Maolin Du, Zaihua Wang & Haiyan Hu

Publication information: Maolin Du, Zaihua Wang & Haiyan Hu. Measuring memory with the order of fractional derivative. Scientific Reports 3, 3431; doi:10.1038/srep03431 (2013).

http://www.nature.com/articles/srep03431

Abstract

Fractional derivative has a history as long as that of classical calculus, but it is much less popular than it should be. What is the physical meaning of fractional derivative? This is still an open problem. In modeling various memory phenomena, we observe that a memory process usually consists of two stages. One is short with permanent retention, and the other is governed by a simple model of fractional derivative. With the numerical least square method, we show that the fractional model perfectly fits the test data of memory phenomena in different disciplines, not only in mechanics, but also in biology and psychology. Based on this model, we find that a physical meaning of the fractional order is an index of memory.

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The End of This Issue

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