FDA Express

FDA Express    Vol. 28, No. 2, Aug. 30, 2018


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Editors: http://jsstam.org.cn/fda/Editors.htm

Institute of Soft Matter Mechanics, Hohai University
For contribution: suxianglong1303@hhu.edu.cn, fdaexpress@hhu.edu.com

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PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol28_No2_2018.pdf


◆  Latest SCI Journal Papers on FDA

(Searched on Aug. 30, 2018)


  Call for Papers

Special Issue on Advances in Fractional Differential Equations (V): Time-space fractional PDEs


◆  Books

Non-Integer Order Calculus and its Applications


◆  Journals

Journal of Sound and Vibration

Applied Mathematical Modelling


  Paper Highlight

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

A spatial fractional seepage model for the flow of non-Newtonian fluid in fractal porous medium


  Websites of Interest

Fractal derivative and operators and their applications

Fractional Calculus & Applied Analysis







 Latest SCI Journal Papers on FDA


(Searched on Aug. 30, 2018)


A fractional motion diffusion model for a twice-refocused spin-echo pulse sequence
By: Karaman, M Muge; Zhou, Xiaohong Joe
NMR in biomedicine Pages: e3960 Published: 2018-Aug-22 (Epub 2018 Aug 22)

Optical excitation fractional Fourier transform (FrFT) based enhanced thermal-wave radar imaging (TWRI).
By: Wang, Fei; Wang, Yonghui; Liu, Junyan; etc.
Optics express Volume: 26  Issue: 17  Pages: 21403-21417  Published: 2018-Aug-20

Periodic boundary value problems for fractional semilinear integro-differential equations with non-instantaneous impulses
By: Zhu, Bo; Liu, Lishan
BOUNDARY VALUE PROBLEMS  Document number: 128  Published: AUG 17 2018

An efficient algorithm based on Gegenbauer wavelets for the solutions of variable-order fractional differential equations
By: Usman, Muhammad; Hamid, Muhammad; Ul Haq, Rizwan; etc.
EUROPEAN PHYSICAL JOURNAL PLUS  Volume: 133  Issue: 8  Document number: 327  Published: AUG 17 2018

Robust consensus of fractional-order multi-agent systems with input saturation and external disturbances
By: Chen, Lin; Wang, Yan-Wu; Yang, Wu; etc.
NEUROCOMPUTING Volume: 303 Pages: 11-19 Published: AUG 16 2018

Optical solitons, self-focusing, and wave collapse in a space-fractional Schrodinger equation with a Kerr-type nonlinearity
By: Chen, Manna; Zeng, Shihao; Lu, Daquan; etc.
PHYSICAL REVIEW E Volume: 98 Issue: 2 Document number: 022211 Published: AUG 15 2018

A generalized Laguerre spectral Petrov-Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain
By: Yu, Hao; Wu, Boying; Zhang, Dazhi
APPLIED MATHEMATICS AND COMPUTATION Volume: 331 Pages: 96-111 Published: AUG 15 2018

A non-polynomial numerical scheme for fourth-order fractional diffusion-wave model
By: Li, Xuhao; Wong, Patricia J. Y.
APPLIED MATHEMATICS AND COMPUTATION Volume: 331 Pages: 80-95 Published: AUG 15 2018


Time fractional modified anomalous sub-diffusion equation with a nonlinear source term through locally applied meshless radial point interpolation
By: Shivanian, Elyas; Jafarabadi, Ahmad
MODERN PHYSICS LETTERS B Volume: 32 Issue: 22 Document number: 1850251 Published: AUG 10 2018


A direct discontinuous Galerkin method for fractional convection-diffusion and Schrodinger-type equations
By: Aboelenen, Tarek
EUROPEAN PHYSICAL JOURNAL PLUS Volume: 133 Issue: 8 Document number: 316 Published: AUG 9 2018


Focus Point on Modelling Complex Real-World Problems with Fractal and New Trends of Fractional Differentiation
By: Atangana, Abdon; Hammouch, Z.; Mophou, G.; etc.
EUROPEAN PHYSICAL JOURNAL PLUS Volume: 133 Issue: 8 Document number: 315 Published: AUG 7 2018


Modeling and analysis of the fractional HBV model with Atangana-Baleanu derivative
By: Ullah, Saif; Khan, Muhammad Altaf; Farooq, Muhammad
EUROPEAN PHYSICAL JOURNAL PLUS Volume: 133 Issue: 8 Document number: 313 Published: AUG 6 2018


MHD mixed convection Poiseuille flow in a porous medium: New trends of Caputo time fractional derivatives in heat transfer problems
By: Khan, Ilyas; Shah, Nehad Ali; Nigar, Niat; etc.
EUROPEAN PHYSICAL JOURNAL PLUS Volume: 133 Issue: 8 Document number: 299 Published: AUG 2 2018

White Blood Cell Extraction on Fractional Calculus and Gradient Vector Flow Snake for Leukocyte Classification on Support Vector Machines
By: Zhang Guangnan; Wang Weixing; Lang Fangnian; etc.
JOURNAL OF MEDICAL IMAGING AND HEALTH INFORMATICS Volume: 8 Issue: 6 Pages: 1249-1257 Published: AUG 2018


Evaluation of classic and fractional models as constitutive relations for carbon black-filled rubber
By: Yin, Boyuan; Hu, Xiaoling; Song, Kui
JOURNAL OF ELASTOMERS AND PLASTICS Volume: 50 Issue: 5 Pages: 463-477 Published: AUG 2018

Formulation of thermodynamically consistent fractional Burgers models
By: Okuka, Aleksandar S.; Zorica, Dusan
ACTA MECHANICA Volume: 229 Issue: 8 Pages: 3557-3570 Published: AUG 2018


Two-Parameter Mittag-Leffler Solution of Space Fractional Advection-Diffusion Equation for Sediment Suspension in Turbulent Flows
By: Kundu, Snehasis
JOURNAL OF ENVIRONMENTAL ENGINEERING Volume: 144 Issue: 8 Document number: 06018005 Published: AUG 2018

Integer and Fractional Order-Based Viscoelastic Constitutive Modeling to Predict the Frequency and Magnetic Field-Induced Properties of Magnetorheological Elastomer
By: Poojary, Umanath R.; Gangadharan, K. V.
JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME Volume: 140 Issue: 4 Document number: 041007 Published: AUG 2018


Stokes' second problem of viscoelastic fluids with constitutive equation of distributed-order derivative
By: Duan, Jun-Sheng; Qiu, Xiang
APPLIED MATHEMATICS AND COMPUTATION Volume: 331 Pages: 130-139 Published: AUG 15 2018






Call for Papers


Special Issue on Advances in Fractional Differential Equations (V): Time-space fractional PDEs

Computers & Mathematics with Applications (Published by Elsevier, impact factor: 1.860)


In the past forty years, fractional calculus had played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory, and signal and image processing. Moreover, it has been found that the dynamical behavior of many complex systems can be properly described by fractional order models. Such models are interesting for engineers and physicists but also for mathematicians. The most important among such models are those described by partial differential equations containing fractional derivatives. Their evolutions behave in a much more complex way than in the classical integer-order case and the study of the corresponding theory, numerical methods and applications is a hugely demanding task. In the past few years, the increase of the subject is witnessed by hundreds of research papers, several monographs, many international conferences.

This is the fifth special issue on Advances in Fractional Differential Equations of the journal CAMWA. This special issue shall deal with some new and different topics with high current interest falling within the scope of the CAMWA, and attract more attention from contributors and readers.

Topics of special issue:

Theory, Theory, numerical methods and applications for fractional PDEs in multiple space dimension
Submission Guidelines:

Manuscripts should be submitted online through EES at the following link: http://ees.elsevier.com/camwa/ . Please select "SI: Fractional PDEs" when you reach the "Select Article Type" step in the submission process, and select "Yong Zhou, Managing Guest Editor (SI: Time-fractional PDEs) " as the Requested Editor. All papers will be peer reviewed. There are no page charges.
Be advised that each author may submit at most two manuscripts to this special issue either as a corresponding author or contributing author.
Important Dates:

Submission Deadline: 31 Oct. 2018

Guest Editors:

Professor Yong Zhou

School of Mathematics and Computational Science
Xiangtan University
XiangtanHunan 411105
P.R. China


Professor Michal Feckan 
Department of Mathematical Analysis and Numerical Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University


Professor Fawang Liu

School of Mathematical Sciences

Queensland University of Technology



Professor J. A. Tenreiro Machado 
Department of Electrical Engineering
ISEP-Institute of Engineering Polytechnic of Porto










Non-Integer Order Calculus and its Applications

(Piotr Ostalczyk, Dominik Sankowski, Jacek Nowakowski (Eds.))

Details: https://link.springer.com/book/10.1007/978-3-319-78458-8.

Book Description

The book includes papers presented at 9th International Conference on Non-integer Order Calculus and Its Applications - 2017 (RRNR 2017), as one of all RRNR Conferences hold in Poland.

The stuff is divided into three parts, focused on:

– Mathematical foundations (7 papers),

– Fractional systems analysis and synthesis (12 papers),

– System modeling (3 papers).

It is a useful resource for fractional calculus scientific community.


The Contents is available at: https://link.springer.com/book/10.1007/978-3-319-78458-8#toc.







Journal of Sound and Vibration



Flutter analysis of a flag of fractional viscoelastic material

Ming Chen, Lai-Bing Jia, Xiao-Peng Chen, Xie-Zhen Yin

Active vibration suppression of a novel airfoil model with fractional order viscoelastic constitutive relationship

Qi Liu, Yong Xu, Jürgen Kurths

A nonlinear and fractional derivative viscoelastic model for rail pads in the dynamic analysis of coupled vehicle–slab track systems

Shengyang Zhu, Chengbiao Cai, Pol D. Spanos

Finite element analysis of vibrating linear systems with fractional derivative viscoelastic models

Silvio Sorrentino, Alessandro Fasana

Dynamic assessment of nonlinear typical section aeroviscoelastic systems using fractional derivative-based viscoelastic model

T. P. Sales, Flávio D. Marques, Daniel A. Pereira, Domingos A. Rade

Statistical origins of fractional derivatives in viscoelasticity

Anindya Chatterjee

Five-parameter fractional derivative model for polymeric damping materials

T. Pritz

The analysis of the impact response of a thin plate via fractional derivative standard linear solid model

Yury A. Rossikhin, Marina V. Shitikova

Dispersion curves for 3D viscoelastic beams of solid circular cross section with fractional derivatives

Tsuneo Usuki






Applied Mathematical Modelling



Numerical inversion of the fractional derivative index and surface thermal flux for an anomalous heat conduction model in a multi-layer medium

Shanzhen Chen, Fawang Liu, Ian Turner, Xiuling Hu

Macroscopic and microscopic anomalous diffusion in comb model with fractional dual-phase-lag model

Lin Liu, Liancun Zheng, Yanping Chen

A fractional order derivative based active contour model for inhomogeneous image segmentation

Bo Chen, Shan Huang, Zhengrong Liang, Wensheng Chen, Binbin Pan

Unstructured mesh finite difference/finite element method for the 2D time-space Riesz fractional diffusion equation on irregular convex domains

Libo Feng, Fawang Liu, Ian Turner, Qianqian Yang, Pinghui Zhuang

A spatial-fractional thermal transport model for nanofluid in porous media

Mingyang Pan, Liancun Zheng, Fawang Liu, Chunyan Liu, Xuehui Chen

A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete

Yanni Bouras, Dušan Zorica, Teodor M. Atanacković, Zora Vrcelj

Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative

Qi Haitao, Xu Mingyu

Nonlinear dynamic analysis of viscoelastic beams using a fractional rheological model

Olga Martin

Decay of potential vortex for a viscoelastic fluid with fractional Maxwell model

M. Khan, S. Hyder Ali, C. Fetecau, Haitao Qi

Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects

M. Faraji Oskouie, R. Ansari

Modeling the arterial wall mechanics using a novel high-order viscoelastic fractional element

J. M. Pérez Zerpa, A. Canelas, B. Sensale, D. Bia Santana, R. L. Armentano

Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid

Ye Tang, Yaxin Zhen, Bo Fang

Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates

Chung-Sik Sin, Liancun Zheng, Jun-Sik Sin, Fawang Liu, Lin Liu

Thermo-viscoelastic materials with fractional relaxation operators

M. A. Ezzat, A. S. El-Karamany, A. A. El-Bary







 Paper Highlight

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

Jaishankar, Aditya; McKinley, Gareth H.

Publication information: JOURNAL OF RHEOLOGY Volume: 58 Issue: 6 Pages: 1751-1788 Published: NOV-DEC 2014




The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally in terms of a Mittag-Leffler function. However, these fractional constitutive models cannot describe the nonlinear behavior of such power-law materials. We use the example of Xanthan gum to show how predictions of nonlinear viscometric properties, such as shear-thinning in the viscosity and in the first normal stress coefficient, can be quantitatively described in terms a nonlinear fractional constitutive model. We adopt an integral K-BKZ framework and suitably modify it for power-law materials exhibiting Mittag-Leffler type relaxation dynamics at small strains. Only one additional parameter is needed to predict nonlinear rheology, which is introduced through an experimentally measured damping function. Empirical rules such as the Cox-Merz rule and Gleissle mirror relations are frequently used to estimate the nonlinear response of complex fluids from linear rheological data. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets, or shift factors, that can be observed between experimental data and the predicted nonlinear response. We also demonstrate how an appropriate choice of fractional constitutive model and damping function results in a nonlinear viscoelastic constitutive model that predicts a flow curve identical to the elastic Herschel-Bulkley model. This new constitutive equation satisfies the Rutgers-Delaware rule, which is appropriate for yielding materials. This K-BKZ framework can be used to generate canonical three-element mechanical models that provide nonlinear viscoelastic generalizations of other empirical inelastic models such as the Cross model. In addition to describing nonlinear viscometric responses, we are also able to provide accurate expressions for the linear viscoelastic behavior of complex materials that exhibit strongly shear-thinning Cross-type or Carreau-type flow curves. The findings in this work provide a coherent and quantitative way of translating between the linear and nonlinear rheology of multiscale materials, using a constitutive modeling approach that involves only a few material parameters.





A spatial fractional seepage model for the flow of non-Newtonian fluid in fractal porous medium

Yang, Xu; Liang, Yingjie; Chen, Wen

Publication information: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 65 Pages: 70-78 Published: DEC 2018




In the present study, a fractional seepage model (FSM) is proposed for non-Newtonian fluid via spatial fractional derivative to characterize the non-local characteristics of the non Newtonian fluid in space and the fractal attributes of the porous medium. The analytical expressions of the permeability and the resistance are derived, in which each parameter contains clear physical meaning. The comparison between the empirical equations and our model with respect to available experimental data verifies the predictive capability of the proposed model. In addition, this study makes the first attempt to bridge the relation between the fractional derivative order and the fractal dimension of tortuosity, and may reveal the correlation between the memory of the complex fluid and characteristic pattern of the microstructure. (C) 2018 Elsevier B.V. All rights reserved.





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