FDA Express

Covering fractional order theory, simulation and experiments, this book explains how fractional order modeling and fractional order controller design compares favorably with traditional velocity and position control systems. The authors systematically compare the two approaches using applied fractional calculus. Stability theory in fractional order controllers design is also analyzed. The book also covers key topics including: fractional order disturbance cancellation and adaptive learning control studies for external disturbances; optimization approaches for nonlinear system control and design schemes with backlash and friction. Illustrations and experimental validations are included for each of the proposed control schemes to enable readers to develop a clear understanding of the approaches covered, and move on to apply them in real-world scenarios.

More information on this book can be found by the following link: http://www.doc88.com/p-4939022504740.html

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Lévy Matters II

Serge Cohen, Alexey Kuznetsov, Andreas E. Kyprianou, Victor Rivero

Book Description

This second volume of the series “Levy Matters” consists of two surveys of two topical areas, namely Fractional Levy Fields by Serge Cohen and the Theory of Scale Functions for Spectrally Negative Levy Processes by Alexey Kuznetsov,Andreas Kyprianou and Victor Rivero. Roughly speaking, irregularity is a crucial aspect of random phenomena that appears in many different contexts. An important issue in this direction is to offer tractable mathematical models that encompass the variety of observed behaviors in applications. Fractional Levy fields are constructed by integration of Levy random measures; somehow they interpolate between Gaussian and stable random fields. They exhibit a number of interesting features including local asymptotic selfsimilarity and multi-fractional aspects. Calibration techniques and simulation of fractional Levy fields constitute important elements for many applications. A real-valued Levy process is spectrally negative when it has no positive jumps. In this situation, the distribution of several variables related to the first exit-time from a bounded interval can be specified in terms of the so-called scale functions; the latter also play a fundamental role in other aspects of the theory. Scale functions are characterized by their Laplace transform, but in general no explicit formula is known, and therefore it is crucial in many applications to gather formation about their asymptotic behavior and regularity and to provide efficient numerical methods to compute them. 　

More information on this book can be found by the following link: http://link.springer.com/book/10.1007/978-3-642-31407-0

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Journals

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Applied Mathematical Modelling

Volume 38, Issue 15–16 (selected)

Numerical simulation for the three-dimension fractional sub-diffusion equation

J. Chen, F. Liu, Q. Liu, X. Chen, V. Anh, I. Turner, K. Burrage

An interval uncertain optimization method for vehicle suspensions using Chebyshev metamodels

Jinglai Wu, Zhen Luo, Yunqing Zhang, Nong Zhang

Convolution quadrature time-domain boundary element method for 2-D fluid-saturated porous media

T. Saitoh, F. Chikazawa, S. Hirose

Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories

Feng Lin, Yang Xiang

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Qianqian Yang, Ian Turner, Timothy Moroney, Fawang Liu

Modelling and identifying the parameters of a magneto-rheological damper with a force-lag phenomenon

G.R. Peng, W.H. Li, H. Du, H.X. Deng, G. Alici

Camouflage devices with simplified material parameters based on conformal transformation acoustics

Chunyu Ren, Zhihai Xiang

A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying

H.C.P. Karunasena, W. Senadeera, Y.T. Gu, R.J. Brown

Higher order finite difference method for the reaction and anomalous-diffusion equation

Changpin Li, Hengfei Ding

A new kernel function for SPH with applications to free surface flows

X.F. Yang, S.L. Peng, M.B. Liu
A response-surface-based structural reliability analysis method by using non-probability convex model

Y.C. Bai, X. Han, C. Jiang, R.G. Bi

Efficient numerical schemes for fractional sub-diffusion equation with the spatially variable coefficient

Xuan Zhao, Qinwu Xu

Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation

P. Zhuang, F. Liu, I. Turner, Y.T. Gu

A new fractional finite volume method for solving the fractional diffusion equation

F. Liu, P. Zhuang, I. Turner, K. Burrage, V. Anh

Transient air flow and heat transfer in a triangular enclosure with a conducting partition

Suvash C. Saha, Y.T. Gu

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Fractional Calculus and Applied Analysis

Volume 17, Issue 4

A theorem of uniqueness of the solution of nonlocal evolution boundary value problem

Yulian Tsankov

Viscoelastic flows with fractional derivative models: Computational approach by convolutional calculus of Dimovski

Emilia Bazhlekova, Ivan Bazhlekov

From the hyper-Bessel operators of Dimovski to the generalized fractional calculus

Virginia Kiryakova

A family of hyper-Bessel functions and convergent series in them

Jordanka Paneva-Konovska

Multiple solutions to boundary value problem for impulsive fractional differential equations

Rosana Rodríguez-López, Stepan Tersian

Cauchy problems for some classes of linear fractional differential equations

Teodor Atanackovic, Diana Dolicanin

Extending the Stieltjes transform II

Dennis Nemzer

Nonstandard Gauss—Lobatto quadrature approximation to fractional derivatives

Shahrokh Esmaeili, Gradimir V. Milovanovic

On the operational solutions of fuzzy fractional differential equations

Djurdjica Takači, Arpad Takači

Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

Zhiyuan Li, Yuri Luchko, Masahiro Yamamoto

New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions

Ali H. Bhrawy, Yahia A. Alhamed

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

Shengli Xie

On the existence of blow up solutions for a class of fractional differential equations

Zhanbing Bai, YangQuan Chen, Hairong Lian

Rhapsody in fractional

J. Tenreiro Machado, Antnio M. Lopes

Reflection symmetric Erdélyi-Kober type operators — A quasi-particle interpretation

Richard Herrmann

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Paper Highlight
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Basic theory of fractional differential equations

V. Lakshmikanthama, A.S. Vatsala

Publication information: V. Lakshmikanthama, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Analysis: Theory, Methods & Applications, 2008, 69(8), 2677-2682.

http://www.sciencedirect.com/science/article/pii/S0362546X07005834

Abstract

In this paper, the basic theory for the initial value problem of fractional differential equations involving Riemann-Liouville differential operators is discussed employing the classical approach. The theory of inequalities, local existence, extremal solutions, comparison result and global existence of solutions are considered.

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Integration and differentiation to a variable fractional order

Stefan G. Samko and Bertram Ross

Publication information: S. G. Samko and B. Ross. Integration and differentiation to a variable fractional order, Integr. Trans. Spec. Funct. 1, 277-300, 1993.

http://www.tandfonline.com/doi/abs/10.1080/10652469308819027

Abstract

Integration and differentiation of functions to a variable order (f^n (x)) is studied in two ways: 1) using the Riemann-Liouville definition, 2) using Fourier transforms. Some properties and the inversion formula are obtained.

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The End of This Issue

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