FDA Express

FDA Express    Vol. 31, No. 3, June 30, 2019

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

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↑  Latest SCI Journal Papers on FDA

(Searched on June 30, 2019)

  Call for Papers

Training School: Computational Methods for Fractional-Order Problems

↑  Books

HAUSDORFF CALCULUS: Applications to Fractal Systems

↑  Journals

International Journal of Solids and Structures

International Journal of Engineering and Science

  Paper Highlight

Frequency domain identification of the fractional Kelvin-Voigt*s parameters for viscoelastic materials

A non-local structural derivative model for memristor

  Websites of Interest

Fractal derivative and operators and their applications

Fractional Calculus & Applied Analysis


 Latest SCI Journal Papers on FDA


(Searched on June 30, 2019)

Fractional Integration and Fat Tails for Realized Covariance Kernels
By: Opschoor, Anne; Lucas, Andre
JOURNAL OF FINANCIAL ECONOMETRICS Volume: 17 Issue: 1 Pages: 66-90 Published: WIN 2019

A preconditioned fast quadratic spline collocation method for two-sided space-fractional partial differential equations
By: Liu, Jun; Fu, Hongfei; Wang, Hong; etc..

By: Shen, Zupei; Han, Zhiqing; Zhang, Qinqin
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S Volume: 12 Issue: 7 Pages: 2115-2125 Published: NOV 2019

By: Wang, Yan; Chen, Guanggan
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 18 Issue: 6 Pages: 3121-3135 Published: NOV 2019

 Controllability of fractional order damped dynamical systems with distributed delays
By: Arthi, G.; Park, Ju H.; Suganya, K.
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 165 Pages: 74-91 Published: NOV 2019

 Numerical solutions of variable order time fractional (1+1)- and (1+2)-dimensional advection dispersion and diffusion models
By: Haq, Sirajul; Ghafoor, Abdul; Hussain, Manzoor
APPLIED MATHEMATICS AND COMPUTATION Volume: 360 Pages: 107-121 Published: NOV 1 2019

 Regional observability for Hadamard-Caputo time fractional distributed parameter systems
By: Cai, Ruiyang; Ge, Fudong; Chen, YangQuan; etc..
APPLIED MATHEMATICS AND COMPUTATION Volume: 360 Pages: 190-202 Published: NOV 1 2019

 Stability and pinning synchronization analysis of fractional order delayed Cohen-Grossberg neural networks with discontinuous activations
By: Pratap, A.; Raja, R.; Cao, J.; etc..
APPLIED MATHEMATICS AND COMPUTATION Volume: 359 Pages: 241-260 Published: OCT 15 2019

 A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrodinger Equations
By: Shi, Yao; Ma, Qiang; Ding, Xiaohua
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS Volume: 11 Issue: 5 Pages: 1219-1247 Published: OCT 2019

 Multiplicity of solutions for fractional p&q-Laplacian system involving critical concave-convex nonlinearities
By: Chen, Wenjing; Gui, Yuyan
APPLIED MATHEMATICS LETTERS Volume: 96 Pages: 81-88 Published: OCT 2019

 Radial symmetry of standing waves for nonlinear fractional Hardy-Schrodinger equation
By: Wang, Guotao; Ren, Xueyan; Bai, Zhanbing; etc..
APPLIED MATHEMATICS LETTERS Volume: 96 Pages: 131-137 Published: OCT 2019

A numerical method for distributed order time fractional diffusion equation with weakly singular solutions
By: Ren, Jincheng; Chen, Hu
APPLIED MATHEMATICS LETTERS Volume: 96 Pages: 159-165 Published: OCT 2019

 Leibniz type rule: psi-Hilfer fractional operator
By: Sousa, J. Vanterler da C.; de Oliveira, E. Capelas

Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction-diffusion equations
By: Zhang, Qifeng; Ren, Yunzhu; Lin, Xiaoman; etc..
APPLIED MATHEMATICS AND COMPUTATION Volume: 358 Pages: 91-110 Published: OCT 1 2019

Response of fractional order on energy ratios at the boundary surface of fluid-piezothermoelastic media
By: Kumar, Rajneesh; Sharma, Poonam
APPLIED MATHEMATICS AND COMPUTATION Volume: 358 Pages: 194-203 Published: OCT 1 2019

Exponentially fitted methods for solving time fractional nonlinear reaction-diffusion equation
By: Zahra, W. K.; Nasr, M. A.; Van Daele, M.
APPLIED MATHEMATICS AND COMPUTATION Volume: 358 Pages: 468-490 Published: OCT 1 2019

Convergence analysis of the Chebyshev-Legendre spectral method for a class of Fredholm fractional integro-differential equations
By: Yousefi, A.; Javadi, S.; Babolian, E.; etc..

 On chaos in the fractional-order Grassi-Miller map and its control
By: Ouannas, Adel; Khennaoui, Amina-Aicha; Grassi, Giuseppe; etc..

 Global synchronization in finite time for fractional-order coupling complex dynamical networks with discontinuous dynamic nodes
By: Jia, You; Wu, Huaiqin
NEUROCOMPUTING Volume: 358 Pages: 20-32 Published: SEP 17 2019

 A new idea of Atangana-Baleanu time fractional derivatives to blood flow with magnetics particles in a circular cylinder: Two phase flow model
By: Ali, Farhad; Yousaf, Salman; Khan, Ilyas; etc..
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS Volume: 486 Document number: UNSP 165282 Published: SEP 15 2019

 A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time-fractional derivative
By: Camilli, Fabio; De Maio, Raul; Iacomini, Elisa
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 477 Issue: 2 Pages: 1019-1032 Published: SEP 15 2019



Call for Papers


Training School: Computational Methods for Fractional-Order Problems

(July 22-26, 2019, Bari, Italy)

The aim of this Training School (July 22-26, 2019, Bari, Italy) is to provide to young researchers the background for understanding the mathematics beyond fractional operators and devise accurate and reliable computational methods. In particular, the development of numerical software for the effective treatment of fractional-order systems will be one of the main assets of the training school with the possibility of organizing some laboratory tutorials.

The preliminary Trainees are: 每 Prof. Kai Diethelm (University of Applied Sciences W邦rzburg-Schweinfurt, Germany): Introduction to FDEs, numerical methods for FDEs; 每 Prof. Roberto Garrappa (University of Bari, Italy): Introduction to fractional calculus, efficient implementation of numerical methods for FDEs; 每 Prof. Guido Maione (Polytechnic University of Bari, Italy): Numerical methods in engineering and control theory; 每 Prof. Maria Luisa Morgado (University of Tr芍s-os-Montes e Alto Douro, Vila Real, Portugal): Collocation methods for FDEs; 每 Prof. Marina Popolizio (Polytechnic University of Bari, Italy): Matrix methods for FDEs and partial FDEs; 每 Prof. Magda Stela Rebelo (Universidade Nova de Lisboa, Portugal): Matlab implementation of collocation methods; 每 Prof. Abner J. Salgado (University of Tennessee, Knoxville, TN, USA): Numerical methods for fractional Laplacian; 每 Prof. Yubin Yan (University of Chester, UK): Numerical methods for fractional partial differential equations.

All details on this Workshop are now available at: https://fractional-systems.eu/ts-2019/.





HAUSDORFF CALCULUS: Applications to Fractal Systems

(Editors: Yingjie Liang, Wen Chen, Wei Cai)

Details: https://www.degruyter.com/view/product/506187#?tdsourcetag=s_pctim_aiomsg


This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.

-Presents the theory and applications of Hausdorff calculus.
-Covers applications in dynamics, statistics, mechanics, and computation.
-Of interest to mathematicians and physicists as well as to engineers.



-Hausdorff diffusion equation

-Statistics on fractals

-Lyapunov stability of Hausdorff derivative non-linear systems

-Hausdorff radial basis function

-Hausdorff PDE modeling

-Local structural derivative


The Contents is available at: https://www.degruyter.com/view/product/506187#?tdsourcetag=s_pctim_aiomsg





International Journal of Solids and Structures


A fractional-order model for aging materials: An application to concrete
Angela Beltempo, Massimiliano Zingales, Oreste S. Bursi, Luca Deseri

A hyperelastic fractional damage material model with memory
Wojciech Sumelka, George Z. Voyiadjis

A 3D fractional elastoplastic constitutive model for concrete material
Dechun Lu, Xin Zhou, Xiuli Du, Guosheng Wang

Fractional order plasticity model for granular soils subjected to monotonic triaxial compression
Yifei Sun, Yang Xiao 

Fractional visco-elastic Euler每Bernoulli beam
M. Di Paola, R. Heuer, A. Pirrotta

Fractional order theory of thermoelasticity
Hany H. Sherief, A. M. A. El-Sayed, A. M. Abd El-Latief

Free energy and states of fractional-order hereditariness
Luca Deseri, Mario Di Paola, Massimiliano Zingales

Lattice with long-range interaction of power-law type for fractional non-local elasticity
Vasily E. Tarasov

Long-range cohesive interactions of non-local continuum faced by fractional calculus
Mario Di Paola, Massimiliano Zingales

A generalized model of elastic foundation based on long-range interactions: Integral and fractional model
M. Di Paola, F. Marino, M. Zingales

Modeling of elastomeric materials using nonlinear fractional derivative and continuously yielding friction elements
Deepak S. Ramrakhyani, George A. Lesieutre, Edward C. Smith

Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation
Y. Z. Povstenko

A fractional order rate approach for modeling concrete structures subjected to creep and fracture
F. Barpi, S. Valente

Damping described by fading memory〞analysis and application to fractional derivative models
Mikael Enelund, Peter Olsson

Time domain modeling of damping using anelastic displacement fields and fractional calculus
Mikael Enelund, George A. Lesieutre

Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws
Mikael Enelund, Lennart Mähler, Kenneth Runesson, B. Lennart Josefson




International Journal of Engineering and Science


The application of the fractional calculus model for dispersion and absorption in dielectrics II. Infrared waves
Andrew W. Wharmby

The application of the fractional calculus model for dispersion and absorption in dielectrics I. Terahertz waves
Andrew W. Wharmby, Ronald L. Bagley

Forced oscillations of a body attached to a viscoelastic rod of fractional derivative type
Teodor M. Atanackovic, Stevan Pilipovic, Dusan Zorica

Modifying Maxwell*s equations for dielectric materials based on techniques from viscoelasticity and concepts from fractional calculus
Andrew W. Wharmby, Ronald L. Bagley

Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod
T. M. Atanackovic, S. Pilipovic, D. Zorica

A new method for solving dynamic problems of fractional derivative viscoelasticity
Yu. A. Rossikhin, M. V. Shitikova

Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models
L. I. Palade, P. Attan谷, R. R. Huilgol, B. Mena



 Paper Highlight

Frequency domain identification of the fractional Kelvin-Voigt*s parameters for viscoelastic materials

M Shabani, K Jahani, M Di Paola, MH Sadeghi 

Publication information: Mechanics of Materials Volume 137, October 2019, 103099



In this work, a new innovative method is used to identify the parameters of fractional Kelvin-Voigt constitutive equation. These parameters are: the order of fractional derivation operator, 0 ≒ 汐 ≒ 1, the coefficient of fractional derivation operator, CV, and the stiffness of the model, KV. A particular dynamic test setup is developed to capture the experimental data. Its outputs are time histories of the excitation and excited accelerations. The investigated specimen is a polymeric cubic silicone gel material known as 汐-gel. Two kinds of experimental excitations are used as random frequencies and constant frequency harmonic excitations. In this study, experimental frequency response functions confirm that increasing the static preload changes the behavior of the investigated viscoelastic material and the fractional Kelvin-Voigt model loses its validity by increasing the precompression. It is shown that, for a random frequencies excitation, by transforming from the time domain to the frequency domain the mentioned parameters can be identified. Using the identified parameters, analytical frequency response functions are so close to their experimental counterparts. Also, analytically produced time histories of the test setup*s output for steady-state experimental tests are so close to the captured time histories. The mentioned results validate the procedure of identification.



A non-local structural derivative model for memristor

 Lin Qiu, Wen Chen, Fajie Wang, Ji Lin

Publication information: Chaos, Solitons & Fractals, Volume 126, September 2019, Pages 169-177


The memristor is of great application and significance in the integrated circuit design, the realization of large-capacity non-volatile memories and the neuromorphic systems. This paper firstly proposes the non-local structural derivative memristor model with two-degree-of-freedom increased to portray the memory effect of memristor. Actually, the developed is a more generalized model that will be reduced to the classical one when the fractal characteristic index 汐 = 1. The proposed model is more flexible than the classical ideal memory model and Riemann Liouville memristor model under the same conditions. In addition, the memory effect described by the present scheme could be adjusted by the position parameter 汛. This work provides a new methodology not only to describe the memory effect of the memristor, but also to easily portray the memristor with ultra-weak memory.



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