FDA Express Vol. 28, No. 3, Sep. 30, 2018
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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
◆ Call for Papers
Special Issue on Advances in Fractional Differential Equations (V): Time-space fractional PDEs
◆ Books
Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology
◆ Journals
Applied Mathematics and Computation
Communications in Nonlinear Science and Numerical Simulation
◆ Paper Highlight
Non-local structural derivative Maxwell model for characterizing ultra-slow rheology in concrete
◆ Websites of Interest
Fractal derivative and operators and their applications
Fractional Calculus & Applied Analysis
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Latest SCI Journal Papers on FDA
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Introducing a stress-dependent
fractional nonlinear viscoelastic model for modified asphalt binders
By: Hajikarimi, Pouria; Nejad, Fereidoon Moghadas; Khodaii, Ali; etc.
CONSTRUCTION AND BUILDING MATERIALS Volume: 183 Pages: 102-113 Published:
SEP 20 2018
General fractional integral inequalities for convex and m-convex functions via
an extended generalized Mittag-Leffler function
By: Farid, G.; Khan, K. A.; Latif, N.; etc.
JOURNAL OF INEQUALITIES AND APPLICATIONS Document number: 243 Published:
SEP 15 2018
Response spectrum method for
building structures with viscoelastic dampers described by fractional
derivatives
By: Lewandowski, Roman; Pawlak, Zdzislaw
ENGINEERING STRUCTURES Volume: 171 Pages: 1017-1026 Published: SEP 15 2018
Fully discrete spectral methods for solving time fractional nonlinear
Sine-Gordon equation with smooth and non-smooth solutions
By: Liu, Zeting; Lu, Shujuan; Liu, Fawang
APPLIED MATHEMATICS AND COMPUTATION Volume: 333 Pages: 213-224 Published: SEP 15
2018
Combination event-triggered adaptive networked synchronization communication for
nonlinear uncertain fractional-order chaotic systems
By: Li, Qiaoping; Liu, Sanyang; Chen, Yonggang
APPLIED MATHEMATICS AND COMPUTATION Volume: 333 Pages: 521-535 Published: SEP 15
2018
External force estimation of a piezo-actuated compliant mechanism based on a
fractional order hysteresis model
By: Zhu, Zhiwei; To, Suet; Li, Yangmin; etc.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING Volume: 110 Pages: 296-306 Published:
SEP 15 2018
An efficient nonpolynomial spline method for distributed order fractional
subdiffusion equations
By: Li, Xuhao; Wong, Patricia J. Y.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES Volume: 41 Issue: 13 Pages:
4906-4922 Published: SEP 15 2018
Suspension concentration distribution in turbulent flows: An analytical study
using fractional advection-diffusion equation
By: Kundu, Snehasis
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 506 Pages: 135-155
Published: SEP 15 2018
Vibration active control of structure with parameter perturbation using
fractional order positive position feedback controller
By: Niu, Wenchao; Li, Bin; Xin, Tao; etc.
JOURNAL OF SOUND AND VIBRATION Volume: 430 Pages: 101-114 Published: SEP 15 2018
On generalized and fractional derivatives and their applications to classical
mechanics
By: Mingarelli, Angelo B.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL Volume: 51 Issue: 36 Document
number: 365204 Published: SEP 7 2018
Dynamics of Gaussian beam modeled by fractional Schrodinger equation with a
variable coefficient
By: Zang, Feng; Wang, Yan; Li, Lu
OPTICS EXPRESS Volume: 26 Issue: 18 Pages: 23740-23750 Published: SEP 3 2018
Riesz Fractional Based Model for Enhancing License Plate Detection and
Recognition
By: Raghunandan, K. S.; Shivakumara, Palaiahnakote; Jalab, Hamid A.; etc.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY Volume: 28 Issue:
9 Pages: 2276-2288 Published: SEP 2018
MHD fractional Jeffrey's fluid flow in the presence of thermo diffusion, thermal
radiation effects with first order chemical reaction and uniform heat flux
By: Imran, M. A.; Miraj, Fizza; Khan, I.; etc.
RESULTS IN PHYSICS Volume: 10 Pages: 10-17 Published: SEP 2018
A modern approach of Caputo-Fabrizio time-fractional derivative to MHD free
convection flow of generalized second-grade fluid in a porous medium
By: Sheikh, Nadeem Ahmad; Ali, Farhad; Khan, Ilyas; etc.
NEURAL COMPUTING & APPLICATIONS Volume: 30 Issue: 6 Pages: 1865-1875 Published:
SEP 2018
A nonconvex fractional order variational model for multi-frame image
super-resolution
By: Laghrib, A.; Ben-Loghfyry, A.; Hadri, A.; etc.
SIGNAL PROCESSING-IMAGE COMMUNICATION Volume: 67 Pages: 1-11 Published: SEP 2018
Robust synchronization of uncertain fractional-order chaotic systems with
time-varying delay
By: Mohammadzadeh, Ardashir; Ghaemi, Sehraneh
NONLINEAR DYNAMICS Volume: 93 Issue: 4 Pages: 1809-1821 Published: SEP 2018
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Call for Papers
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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.
Guest Editors:
Professor Yong Zhou
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
Professor
J. A. Tenreiro Machado
Department of Electrical Engineering
ISEP-Institute of Engineering Polytechnic of Porto
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Books
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Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology
(Abdon Atangana)
Details:
https://www.sciencedirect.com/book/9780128096703/fractional-operators-with-constant-and-variable-order-with-application-to-geo-hydrology#book-infoBook Description
Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author’s analyses, the book proposes new techniques for groundwater remediation, including guidelines on how chemical companies can be positioned in any city to avoid groundwater pollution.
Chapters
-Aquifers and Their Properties
-Principle of Groundwater Flow
-Groundwater Pollution
-Limitations of Groundwater Models With Local Derivative
-Fractional Operators and Their Applications
-Regularity of a General Parabolic Equation With Fractional Differentiation
-Applications of Fractional Operators to Groundwater Models
-Models of Groundwater Pollution With Fractional Operators
-Fractional Variable Order Derivatives
-Groundwater Flow Model in Self-similar Aquifer With Atangana–Baleanu Fractional Operators
-Groundwater Flow Within a Fracture, Matrix Rock and Leaky Aquifers: Fractal Geometry
-Modeling Groundwater Pollution With Variable Order Derivatives
-Groundwater Recharge Model With Fractional Differentiation
-Atangana Derivative With Memory and Application
-References
The Contents is available at:
https://www.sciencedirect.com/book/9780128096703/fractional-operators-with-constant-and-variable-order-with-application-to-geo-hydrology#book-info.
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Journals
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Applied Mathematics and Computation
(Selected)
Yuan-Ming Wang, Lei Ren
A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation
Mohammad Hossein Heydari, Zakieh Avazzadeh, Malih Farzi Haromi
Hugo Aguirre-Ramos, Juan Gabriel Avina-Cervantes, Ivan Cruz-Aceves, José Ruiz-Pinales, Sergio Ledesma
Meshless spectral method for solution of time-fractional coupled KdV equations
Manzoor Hussain, Sirajul Haq, Abdul Ghafoor
A note on Katugampola fractional calculus and fractal dimensions
S. Verma, P. Viswanathan
Local RBF-FD technique for solving the two-dimensional modified anomalous sub-diffusion equation
Hossein Pourbashash, Mahmood Khaksar-e Oshagh
Macroeconomic models with long dynamic memory: Fractional calculus approach
Vasily E. Tarasov, Valentina V. Tarasova
Numerical analysis for Navier–Stokes equations with time fractional derivatives
Jun Zhang, JinRong Wang
A nonlinear viscoelastic fractional derivative model of infant hydrocephalus
K. P. Wilkie, C. S. Drapaca, S. Sivaloganathan
[Back]
Communications in Nonlinear Science and Numerical Simulation
(Selected)
On an accurate discretization of a variable-order fractional reaction-diffusion equation
Mojtaba Hajipour, Amin Jajarmi, Dumitru Baleanu, HongGuang Sun
Emergence of death islands in fractional-order oscillators via delayed coupling
Rui Xiao, Zhongkui Sun, Xiaoli Yang, Wei Xu
Fractional calculus via Laplace transform and its application in relaxation processes
E. Capelas de Oliveira, S. Jarosz, J. Vaz
Approximate conservation laws for fractional differential equations
Stanislav Yu. Lukashchuk
Simulations of variable concentration aspects in a fractional nonlinear viscoelastic fluid flow
Amer Rasheed, Muhammad Shoaib Anwar
Extremely low order time-fractional differential equation and application in combustion process
Qinwu Xu, Yufeng Xu
Ana R. M. Carvalho, Carla M. A. Pinto
Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids
Xiaoping Wang, Haitao Qi, Bo Yu, Zhen Xiong, Huanying Xu
Cheng-shi Liu
Fractal calculus involving gauge function
Alireza K. Golmankhaneh, Dumitru Baleanu
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Paper Highlight
Lu, Changna; Fu, Chen; Yang, Hongwei
Publication information: APPLIED MATHEMATICS AND COMPUTATION Volume: 327 Pages: 104-116 Published: JUN 15 2018
Abstract
Construct fractional order model to describe Rossby solitary waves can provide more pronounced effects and deeper insight for comprehending generalization and evolution of Rossby solitary waves in stratified fluid. In the paper, from the quasi-geostrophic vorticity equation with dissipation effect and complete Coriolis force, based on the multi-scale analysis and perturbation method, a classical generalized Boussinesq equation is derived to describe the Rossby solitary waves in stratified fluid. Further, by employing the reduction perturbation method, the semi-inverse method, the Agrawal method, we derive the Euler-lagrangian equation of classical generalized Boussinesq equation and obtain the time-fractional generalized Boussinesq equation. Without dissipation effect, by using Lie group analysis method, the conservation laws of time-fractional Boussinesq equation are given. Finally, with the help of the improved (G'/G) expansion method, the exact solutions of the above equation are generated. Meanwhile, in order to consider the dissipation effect, we have to derive the approximate solutions by adopting the New Iterative Method. We remark that the fractional order model can open up a new window for better understanding the waves in fluid.
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Non-local structural derivative Maxwell model for characterizing ultra-slow rheology in concrete
Xianglong Su, Wen Chen, Wenxiang Xu, Yingjie Liang
Publication information: Construction and Building Materials, Volume 190, 30 November 2018, Pages 342-348
Abstract
Ultra-slow rheological phenomena have widely been observed in engineering materials. The logarithmic law is normally used to describe the slow rheology, but it does not work well for the long-term ultra-slow rheology. In this paper, we devise a new Maxwell-type viscoelastic model to capture the ultra-slow rheology by using the non-local structural derivative, where the inverse Mittag-Leffler (ML) structural function is adopted. The viscoelastic responses of the ultra-slow Maxwell model are analytically derived, including creep and relaxation. The logarithmic creep law can be regarded as a special case of the ultra-slow Maxwell model. In addition, the proposed model is tested by several experimental data of concrete. Compared with the existed models, the present ultra-slow Maxwell model shows the reasonable accuracy. The derived results indicate that the non-local structural derivative involving the inverse ML function is feasible to capture the ultra-slow rheology of concrete.
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