FDA Express

FDA Express    Vol. 22, No. 1, Jan 15, 2017


All issues: http://em.hhu.edu.cn/fda/

Editors: http://em.hhu.edu.cn/fda/Editors.htm

Institute of Soft Matter Mechanics, Hohai University
For contribution: heixindong@hhu.edu.cn, pangguofei2008@126.com

For subscription: http://em.hhu.edu.cn/fda/subscription.htm

PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol22_No1_2017.pdf


◆  Latest SCI Journal Papers on FDA

(Searched on Jan 15, 2017)


  Call for papers

Special Issue: Advances on Computational Fractional Partial Differential Equations


◆  Books

Discrete Fractional Calculus

Discrete Fractional Calculus: Applications in Control and Image Processing


◆  Journals

Journal of Automatica Sinica

Journal of Computational Physics


  Paper Highlight

Mathematical modelling of fractional order circuit elements and bioimpedance applications

A new variational approach for restoring images with multiplicative noise


  Websites of Interest

Fractal derivative and operators and their applications

Fractional Calculus & Applied Analysis





 Latest SCI Journal Papers on FDA


(Searched on Jan 15, 2016)

Mathematical modelling of fractional order circuit elements and bioimpedance applications

By: Angel Moreles, Miguel; Lainez, Rafael


Numerical study of the process of nonlinear supratransmission in Riesz space-fractional sine-Gordon equations

By:Macias-Diaz, J. E.


A radial symmetry and Liouville theorem for systems involving fractional Laplacian

By: Li, Dongsheng; Li, Zhenjie

FRONTIERS OF MATHEMATICS IN CHINA Volume: 12 Issue: 2 Pages: 389-402 Published: APR 2017

Direct Low Order Rational Approximations for Fractional Order Systems in Narrow Frequency Band: A Fix-Pole Method

By: Liang, Yinshan; Lu, Jiangling

JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS Volume: 26 Issue: 4 Article Number: 1750065 Published: APR 2017

Stability analysis for impulsive fractional hybrid systems via variational Lyapunov method

By: Yang, Ying; He, Yong; Wang, Yong; et al.

Communications in Nonlinear Science and Numerical Simulation Volume: 45 Pages: 140-157 Published: APR 2017


By: He, Huijun; Yin, Zhaoyang

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume: 37 Issue: 3 Pages: 1509-1537 Published: MAR 2017

An approximate solution based on Jacobi polynomials for time-fractional convection-diffusion equation

By: Behroozifar, M.; Sazmand, A.

APPLIED MATHEMATICS AND COMPUTATION Volume: 296 Pages: 1-17 Published: MAR 1 2017

Discrete spline methods for solving two point fractional Bagley-Torvik equation

By:Zahra, W. K.; Van Daele, M

APPLIED MATHEMATICS AND COMPUTATION Volume: 296 Pages: 42-56 Published: MAR 1 2017

Center stable manifold for planar fractional damped equations

By: Wang, JinRong; Fetkan, Michal; Zhou, Yong

APPLIED MATHEMATICS AND COMPUTATION Volume: 296 Pages: 257-269 Published: MAR 1 2017

Implicit Euler approximation of stochastic evolution equations with fractional Brownian motion

By: Kamrani, Minoo; Jamshidi, Nahid






Call for Papers


Special Issue: Advances on Computational Fractional Partial Differential Equations

------ International Journal of Computer Mathematics



The special issue will present the state of the art of the research in the field of Computational Fractional PDEs. This issue solicits high quality original research papers which present and discuss recent advances on computational methods for Fractional PDEs and their applications in Science and Engineering.


Submission Deadlines:
Deadline for submission of full paper: April 01, 2017
Deadline for submission of revised manuscripts: August 01, 2017
Notification of Final acceptance: October 2017
Date of publication: December 2017


Editorial information:

Guest Editor: K.M. Furati , King Fahd University of Petroleum and Minerals, Saudi Arabia

Guest Editor: A.Q.M. Khaliq , Middle Tennessee State University, USA

Guest Editor: Ch. Li, Shanghai University, China

Guest Editor: M. Zayernouri, Michigan State University, USA










Discrete Fractional Calculus

Christopher Goodrich, Allan C. Peterson

Book Description

The continuous fractional calculus has a long history within the broad area of mathematical analysis. Indeed, it is nearly as old as the familiar integer-order calculus. Since its inception, it can be traced back to a question L’Hôpital had asked Leibniz in 1695 regarding the meaning of a one-half derivative; it was not until the 1800s that a firm theoretical foundation for the fractional calculus was provided. Nowadays the fractional calculus is studied both for its theoretical interest as well as its use in applications.

    In spite of the existence of a substantial mathematical theory of the continuous fractional calculus, there was really no substantive parallel development of a discrete fractional calculus until very recently. Within the past five to seven years however, there has been a surge of interest in developing a discrete fractional calculus. This development has demonstrated that discrete fractional calculus has a number of unexpected difficulties and technical complications.

    In this text we provide the first comprehensive treatment of the discrete fractional calculus with up-to-date references. We believe that students who are interested in learning about discrete fractional calculus will find this text to be a useful starting point. Moreover, experienced researchers, who wish to have an up-to-date reference for both discrete fractional calculus and on many related topics of current interest, will find this text instrumental.


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





Discrete Fractional Calculus: Applications in Control and Image Processing

Piotr Ostalczyk

Book Description

The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing.


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










Journal of Automatica Sinica

(Special Issue on Fractional Order Systems and Controls)


The fractional landau model

Bruce J. West ; Malgorzata Turalska

A fractional micro-macro model for crowds of pedestrians based on fractional mean field games

Kecai Cao ; Yangquan Chen ; Daniel Stuart

Fractional order modeling of human operator behavior with second order controlled plant and experiment research

Jiacai Huang ; Yangquan Chen ; Haibin Li ; Xinxin Shi

Fractional modeling and SOC estimation of lithium-ion battery

Yan Ma ; Xiuwen Zhou ; Bingsi Li ; Hong Chen

Fractional modeling and analysis of coupled MR damping system

Bingsan Chen ; Chunyu Li ; Benjamin Wilson ; Yijian Huang

Parameter estimation and topology identification of uncertain general fractional-order complex dynamical networks with time delay

Xiaojuan Chen ; Jun Zhang ; Tiedong Ma

H∞ output feedback control of linear time-invariant fractional-order systems over finite frequency range

Cuihong Wang ; Huanhuan Li ; Yangquan Chen

The ellipsoidal invariant set of fractional order systems subject to actuator saturation: the convex combination form

Kai Chen ; Junguo Lu ; Chuang Li

Constrained swarm stabilization of fractional order linear time invariant swarm systems

Mojtaba Naderi Soorki ; Mohammad Saleh Tavazoei

Improving the control energy in model reference adaptive controllers using fractional adaptive laws

Norelys Aguila-Camacho ; Manuel A. Duarte-mermoud

An approach to design MIMO FO controllers for unstable nonlinear plants

Arturo Rojas-Moreno






Journal of Computational Physics


Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains

Z. Yang, Z. Yuan, Y. Nie, J. Wang, X. Zhu, F. Liu

Fast parareal iterations for fractional diffusion equations

Shu-Lin Wu, Tao Zhou

A higher order non-polynomial spline method for fractional sub-diffusion problems

Xuhao Li, Patricia J.Y. Wong

On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross–Pitaevskii equations with rotation term and nonlocal nonlinear interactions

Xavier Antoine, Qinglin Tang, Yong Zhang

Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

Yue Yu, Paris Perdikaris, George Em Karniadakis

A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation

Xue-lei Lin, Xin Lu, Micheal K. Ng, Hai-Wei Sun

Correction to “What is a fractional derivative?” by Ortigueira and Machado [Journal of Computational Physics, Volume 293, 15 July 2015, Pages 4–13. Special issue on Fractional PDEs]

Udita N. Katugampola

Numerical investigation of a space-fractional model of turbulent fluid flow in rectangular ducts

Alexander G. Churbanov, Petr N. Vabishchevich

Efficient implementation to numerically solve the nonlinear time fractional parabolic problems on unbounded spatial domain

Dongfang Li, Jiwei Zhang

Spectral approximation methods and error estimates for Caputo fractional derivative with applications to initial-value problems

Beiping Duan, Zhoushun Zheng, Wen Cao







 Paper Highlight

Mathematical modelling of fractional order circuit elements and bioimpedance applications

Angel Moreles, Miguel; Lainez, Rafael

Publication information: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 46 Pages: 81-88 Published: MAY 2017




In this work a classical derivation of fractional order circuits models is presented. Generalised constitutive equations in terms of fractional Riemann-Liouville derivatives are introduced in the Maxwell’s equations for each circuit element. Next the Kirchhoff voltage law is applied in a RCL circuit configuration. It is shown that from basic properties of Fractional Calculus, a fractional differential equation model with Caputo derivatives is obtained. Thus standard initial conditions apply. Finally, models for bioimpedance are revisited.




A new variational approach for restoring images with multiplicative noise

A Ullah,W Chen,MA Khan

Publication information: COMPUTERS & MATHEMATICS WITH APPLICATIONS Volume: 71 Issue: 10 Pages: 2034-2050 Published: MAY 2016




This paper proposes a novel variational model for restoration of images corrupted with multiplicative noise. It combines a fractional-order total variational filter with a high-order PDE (Laplacian) norm. The combined approach is able to preserve edges while avoiding the blocky-effect in smooth regions. This strategy minimizes a certain energy subject to a fitting term derived from a maximum a posteriori (MAP). Semi-implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional. To improve the numerical results, we opt for an adaptive regularization parameter selection procedure for the proposed model by using the trial-and-error method. The existence and uniqueness of a solution to the proposed variational model is established. In this study parameter dependence is also discussed. Experimental results demonstrate the effectiveness of the proposed model in visual improvement as well as an increase in the peak signal-to-noise ratio comparing to corresponding PDE methods.







The End of This Issue