FDA Express

Please kindly note that the manuscript must be submitted to http://ees.elsevier.com/amc/ . The authors should select "SI: Advances in FDEs" when you reach the "Choose Article Type" step in the submission process, and select "Yong Zhou" as the Requested Editor.

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Books

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Special Functions in Fractional Calculus and Related Fractional Differintegral Equations

Hari M. Srivastava

Book Description

The subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. It does indeed provide several potentially useful tools for solving differential, integral and differintegral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables.Many books and monographs (and conference proceedings) deal with the subject of fractional calculus and its applications. However, to the best of our knowledge, there does not exist an exclusive work that co-ordinates the disciplines of fractional calculus and special functions in a potentially useful manner. This book is an attempt in that direction and would serve a dual purpose: in providing key formulas and identities involving special functions and also in opening up some novel avenues of applications of fractional calculus.

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

http://books.google.com.hk/books?id=cjzAngEACAAJ&dq=fractional+calculus&hl=zh-CN&sa=X&ei=kphfU7SXBquUiQeL2oDwDA&ved=0CCIQ6AEwADgK

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Fractional Calculus: Theory and Applications

Varsha Daftardar-gejji

Book Description

FRACTIONAL CALCULUS: Theory and Applications deals with differentiation and integration of arbitrary order. The origin of this subject can be traced back to the end of seventeenth century, the time when Newton and Leibniz developed foundations of differential and integral calculus. Nonetheless, utility and applicability of FC to various branches of science and engineering have been realized only in last few decades. Recent years have witnessed tremendous upsurge in research activities related to the applications of FC in modeling of real-world systems. Unlike the derivatives of integral order, the non-local nature of fractional derivatives correctly models many natural phenomena containing long memory and give more accurate description than their integer counterparts. The present book comprises of contributions from academicians and leading researchers and gives a panoramic overview of various aspects of this subject: * Introduction to Fractional Calculus * Fractional Differential Equations * Fractional Ordered Dynamical Systems * Fractional Operators on Fractals * Local Fractional Derivatives * Fractional Control Systems * Fractional Operators and Statistical Distributions * Applications to Engineering

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

http://books.google.com.hk/books?id=fBWYngEACAAJ&dq=fractional+calculus&hl=zh-CN&sa=X&ei=OZlfU-6mD6SRiQej7oCoDg&ved=0CD0Q6AEwBjgK

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Journals

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International Journal of Bifurcation and Chaos

Volume: 24, Number: 04

Correlation Dimension of Fractional Gaussian Noise: New Evidence from Wavelets

Zouhaier Dhifaoui, Hedi Kortas, Samir Benammou

Bifurcation Analysis of a Generic Reaction–Diffusion Turing Model

Ping Liu, Junping Shi, Rui Wang, Yuwen Wang

Effects of Delay and Diffusion on the Dynamics of a Leslie–Gower Type Predator–Prey Model

Jia-Fang Zhang, Xiang-Ping Yan

The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (A, B)

Joan C. Artés, Alex C. Rezende, Regilene D. S. Oliveira

Toward a General Procedure for Extracting Templates from Chaotic Attractors Bounded by High Genus Torus

Martin Rosalie, Christophe Letellier

Implementations of Modified Chaotic Neural Models with Analog Reconfigurable Hardware

Nimet Korkmaz, Recai Kilic

Chaos Entanglement: Leading Unstable Linear Systems to Chaos

Hongtao Zhang, Xinzhi Liu, Xianguo Li

Design and Circuit Implementation of Discrete-Time Chaotic Systems with Modulus of Triangular Wave Functions

Chaowen Shen, Simin Yu, Jinhu Lü

Design and ARM Platform-Based Realization of Digital Color Image Encryption and Decryption via Single State Variable Feedback Control

Hanzhong Zheng, Simin Yu, Jinhu Lü

A Multiaddress Co-Chaos Shift Keying Communication Scheme and Performance Analysis

Zhiliang Zhu, Jingping Song, Yanjie Song, Hai Yu

Global Bifurcation Analysis of a Duffing–Van der Pol Oscillator with Parametric Excitation

Qun Han, Wei Xu, Xiaole Yue

Stochastic and Coherence Resonance in a Dressed Neuron Model

Ying Liu, Xinmin Xu

More Than Three Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Zones in the Plane

Denis De Carvalho Braga, Luis Fernando Mello

Improved Homoclinic Predictor for Bogdanov–Takens Bifurcation

Yu. A. Kuznetsov, H. G. E. Meijer, B. Al Hdaibat, W. Govaerts

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Journal of Applied Nonlinear Dynamics

Volume 3, Issue 1

Comparison Between Davidson-Cole and Frequency-Band Limited Fractional Differentiator I/O Type Transfer Function with Speed and Acceleration Inputs in Path Tracking Design

N. Yousfi, P. Melchior, C. Rekik, N. Derbel, and A. Oustaloup

Dynamics of Bimodality in Vehicular Traffic Flows

Arjun Mullick and Arnab K. Ray

ODE Admitting Two-dimensional Algebras of Dynamic Symmetries

M.I. Timoshin

The Dynamics of the Slow Flow of a Singular Damped Nonlinear System and It Parametric Study

J.O. Maaita, E. Meletlidou, A.F. Vakakis, and V. Rothos

Synchronization and Stability of Surface Acoustic Wave (SAW) Coupled Phase Oscillators and Sensing Applications

Shashank S. Jha and R.D.S. Yadava

Transmission Model for the Co-infection of HIV/AIDS and Tuberculosis

Carla MA Pinto and Ana Carvalho

Low-Frequency Free Vibration of Rods with Finite Strain

A.M. Baghestani, S.J. Fariborz, and S.M. Mousavi

Soliton Solutions for the Modified KdV6, Modified (2+1)-dimensional Boussinesq, and (3+1)-dimensional KdV Equations

Abdul-Majid Wazwaz

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Paper Highlight
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Fractional Derivatives and Special Functions

J. L. Lovoie, T. J. Osler, and R. Tremblay

Publication information: J. L. Lovoie, T. J. Osler, and R. Tremblay, Fractional Derivatives and Special Functions. SIAM Rev., 18(2), 240–268. (29 pages) http://epubs.siam.org/doi/abs/10.1137/1018042

Abstract

The fractional derivative operator is an extension of the familiar derivative operator $D^n $ to arbitrary (integer, rational, irrational, or complex) values of n. The most important representations which have been proposed for this concept are reviewed in this paper. In particular, those representations which appear to be of greatest interest for use in exploring the special functions, are presented in detail. A list of selected formulas and theorems on fractional differentiation is presented. Applications to the summation of series and the evaluation of definite integrals incorporating special functions are mentioned.

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Approximation of Grünwald-Letnikov Fractional Derivative for FDTD Modeling of Cole-Cole Media

Ioannis T. Rekanos and Traianos V. Yioultsis

Publication information: Ioannis T. Rekanos and Traianos V. Yioultsis, Approximation of Grünwald–Letnikov Fractional Derivative for FDTD Modeling of Cole-Cole Media. IEEE TRANSACTIONS ON MAGNETICS, 50(2), 2014, 7004304. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6749142

Abstract

A finite-difference time-domain (FDTD) method for modeling wave propagation in dispersive Cole-Cole media is proposed. The main difficulty in time-domain modeling of a Cole-Cole medium is that the polarization relation that describes its electromagnetic behavior is a differential equation of fractional order. By definition, the fractional derivative of a function is a nonlocal operator and its computation at a time instant involves all previous function values. Thus, the memory demands of a typical FDTD scheme for Cole-Cole media would be high. However, by an appropriate approximation of the Grünwald-Letnikov definition of the fractional derivative, we can implement an FDTD scheme with reasonable memory demands. This is achieved by means of sums of decaying exponentials used to approximate the coefficients that appear in the Grünwald–Letnikov definition. As a result, the FDTD scheme requires the additional storage of a limited number of auxiliary vectors only. The proposed scheme has been applied successfully to the simulation of the excitation of Cole-Cole media by a wideband Gaussian electromagnetic pulse.

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