FDA Express Vol. 30, No. 2, Feb. 28, 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
◆ Call for Papers
Special Issue "Applications of Statistical Thermodynamics"
◆ Books
HAUSDORFF CALCULUS: Applications to Fractal Systems
◆ Journals
Fractional Calculus and Applied Analysis
◆ Paper Highlight
◆ 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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Application of a Legendre collocation method to the space-time variable
fractional-order advection-dispersion equation
By: Mallawi, F.; Alzaidy, J. F.; Hafez, R. M.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 13 Issue: 1 Pages: 324-330
Document number: UNSP 101007 Published: DEC 11 2019
Numerical solutions to systems of fractional Voltera Integro differential
equations, using Chebyshev wavelet method (vol 12, pg 584, 2018)
By: Khan, H.; Arif, M.; Mohyud-Din, S. T.; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 13 Issue: 1 Pages: 286-286
Published: DEC 11 2019
Dynamical analysis of Hilfer-Hadamard type fractional pantograph equations via
successive approximation
By: Vivek, D.; Shah, Kamal; Kanagarajan, K.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 13 Issue: 1 Pages: 225-230
Published: DEC 11 2019
GROUND STATE SOLUTIONS FOR THE FRACTIONAL SCHRODINGER-POISSON SYSTEMS INVOLVING
CRITICAL GROWTH IN R-3
By: Guo, Lun; Huang, Wentao; Jia, Huifang
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 18 Issue: 4 Pages: 1663-1693
Published: JUL 2019
EXISTENCE, MULTIPLICITY AND
CONCENTRATION FOR A CLASS OF FRACTIONAL p&q LAPLACIAN PROBLEMS IN R-N
By: Alves, Claudianor O.; Ambrosio, Vincenzo; Isernia, Teresa
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 18 Issue: 4 Pages: 2009-2045
Published: JUL 2019
A note on efficient preconditioner
of implicit Runge-Kutta methods with application to fractional diffusion
equations
By: Chen, Hao; Wang, Xiaoli; Li, Xiaolin
APPLIED MATHEMATICS AND COMPUTATION Volume: 351 Pages: 116-123 Published: JUN 15
2019
An explicit fourth-order energy-preserving scheme for Riesz space fractional
nonlinear wave equations
By: Zhao, Jingjun; Li, Yu; Xu, Yang
APPLIED MATHEMATICS AND COMPUTATION Volume: 351 Pages: 124-138 Published: JUN 15
2019
The fractional Allen-Cahn equation with the sextic potential
By: Lee, Seunggyu; Lee, Dongsun
APPLIED MATHEMATICS AND COMPUTATION Volume: 351 Pages: 176-192 Published: JUN 15
2019
A numerically efficient and conservative model for a Riesz space-fractional
Klein-Gordon-Zakharov system
By: Hendy, A. S.; Macias-Diaz, J. E.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 71 Pages:
22-37 Published: JUN 15 2019
Variational approach for breathers in a nonlinear fractional Schrodinger
equation
By: Chen, Manna; Guo, Qi; Lu, Daquan; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 71 Pages:
73-81 Published: JUN 15 2019
Distributed consensus tracking of unknown nonlinear chaotic delayed
fractional-order multi-agent systems with external disturbances based on ABC
algorithm
By: Hu, Wei; Wen, Guoguang; Rahmani, Ahmed; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 71 Pages:
101-117 Published: JUN 15 2019
Time-fractional Benjamin-Ono equation for algebraic gravity solitary waves in
baroclinic atmosphere and exact multi-soliton solution as well as interaction
By: Yang, Hongwei; Sun, Junchao; Fu, Chen
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 71 Pages:
187-201 Published: JUN 15 2019
Lamperti transformation - Cure for
ergodicity breaking
By: Magdziarz, Marcin; Zorawik, Tomasz
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 71 Pages:
202-211 Published: JUN 15 2019
Variable order fractional systems
By: Ortigueira, Manuel D.; Valerio, Duarte; Machado, J. Tenreiro
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 71 Pages:
231-243 Published: JUN 15 2019
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Call for Papers
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Special Issue
"Applications of Statistical Thermodynamics"
Entropy (IF:2.305)
Special Issue Information
Dear Colleagues,
Statistical thermodynamics span the bridge between the visible macroscopic world
and the invisible atomistic world to evaluate values of atomistic interaction
parameters with unambiguous physical significance from measured values of state
parameters, such as temperature, pressure and chemical composition under
equilibrium state. Unlike conventional thermodynamics, in which entropy,
enthalpy, and free energy are defined mathematically in terms of state
parameters and thus applicable universally to any system, even without knowing
exactly the nature of compound under consideration, statistical thermodynamic
analysis must be started from unambiguous a priori modeling of compounds under
consideration. When an unrealistic model is chosen at the onset of the
statistical thermodynamic approach, the evaluated parameters are without valid
physical significance. This inherent nature of the statistical thermodynamic
approach might make use of this unique analysis tool somewhat difficult for
experimentalists to use casually. However, there also lies a merit of this
unique analysis tool to a provide feedback channel to check the validity of the
a priori model with reference to the compatibility of the evaluated atomistic
interaction parameter values with the macroscopic state parameter values.
The Guest Editor wishes this Special Issue will attract the attention of authors
who have been working on entropy and enthalpy aspects of materials science, as
well as physicists and chemists using statistical thermodynamics as an analysis
tool.
Prof. Dr. Nobumitsu Shohoji
Guest Editor
Special Issue Editor
Guest Editor
Prof. Dr. Nobumitsu Shohoji
LNEG - Laboratório Nacional de Energia e Geologia, LEN - Laboratório de Energia
Estrada do Paço do Lumiar, 22 1649-038 Lisboa, Portugal
Website | E-Mail
Phone: +351 21 092 9600 (ext. 4234)
Interests: 1. Statistical thermodynamic analysis of non-stoichiometric
interstitial compounds; 2. Synthesis of carbide, nitride and carbo-nitride
(using concentrated solar beam as the heat source as well as using conventional
electric furnace); 3. Formation and characterization of non-equilibrium solid
phases
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and
logging in to this website. Once you are registered, click here to go to the
submission form. Manuscripts can be submitted until the deadline. All papers
will be peer-reviewed. Accepted papers will be published continuously in the
journal (as soon as accepted) and will be listed together on the special issue
website. Research articles, review articles as well as short communications are
invited. For planned papers, a title and short abstract (about 100 words) can be
sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under
consideration for publication elsewhere (except conference proceedings papers).
All manuscripts are thoroughly refereed through a single-blind peer-review
process. A guide for authors and other relevant information for submission of
manuscripts is available on the Instructions for Authors page. Entropy is an
international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript.
The Article Processing Charge (APC) for publication in this open access journal
is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use
good English. Authors may use MDPI's English editing service prior to
publication or during author revisions.
Deadline for manuscript submissions: 30 June 2019
Keywords
-Statistical thermodynamics
-Entropy (configurational, electronic)
-Enthalpy
-Free Energy
-Saddle point approach
-Non-stoichiometry
-Interstitial
-Substitutional
Further information, see https://www.mdpi.com/si/entropy/Statistical_Thermodynamics
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Books
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(Editors: Yingjie Liang, Wen Chen, Wei Cai)
Details: https://www.degruyter.com/view/product/506187#?tdsourcetag=s_pctim_aiomsg
Introduction
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.
Chapters
-Introduction
-Hausdorff diffusion equation
-Statistics on fractals
-Lyapunov stability of Hausdorff derivative non-linear systems
-Hausdorff radial basis function
-Hausdorff PDE modeling
-Local structural derivative
-Perspectives
The Contents is available at:
https://www.degruyter.com/view/product/506187#?tdsourcetag=s_pctim_aiomsg
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Journals
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Fractional Calculus and Applied Analysis
(Volume 21, Issue 5-6 (Oct, Dec 2018))
Fractional calculus’s adventures in Wonderland (Round table held at ICFDA 2018)
Tenreiro Machado, J.A. / Kiryakova, Virginia / Mainardi, Francesco / Momani, Shaher
On modifications of the exponential integral with the Mittag-Leffler function
Mainardi, Francesco / Masina, Enrico
Global solutions to stochastic Volterra equations driven by Lévy noise
Hausenblas, Erika / Kovács, Mihály
Butko, Yana A.
Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems
Gomoyunov, Mikhail I.
Regularity of solutions to space–time fractional wave equations: A PDE approach
Otárola, Enrique / Salgado, Abner J.
Asymptotically periodic solutions for Caputo type fractional evolution equations
Ren, Lulu / Wang, JinRong / Fečkan, Michal
Complex fractional Zener model of wave propagation in R
Atanacković, Teodor M. / Janev, Marko / Konjik, Sanja / Pilipović, Stevan
Maximum principles for time-fractional Cauchy problems with spatially non-local components
Biswas, Anup / Lőrinczi, József
Karp, Dmitrii B. / López, José L.
A further extension of Mittag-Leffler function
Andrić, Maja / Farid, Ghulam / Pečarić, Josip
Frequency-distributed representation of irrational linear systems
Rapaić, Milan R. / Šekara, Tomislav B. / Bošković, Marko Č.
D’Ovidio, Mirko / Vitali, Silvia / Sposini, Vittoria / Sliusarenko, Oleksii / Paradisi, Paolo / Castellani, Gastone / Pagnini, Gianni
Li, Xiuwen / Li, Yunxiang / Liu, Zhenhai / Li, Jing
Finite-time attractivity for semilinear tempered fractional wave equations
Ke, Tran Dinh / Quan, Nguyen Nhu
Geometry of curves with fractional-order tangent vector and Frenet-Serret formulas
Yajima, Takahiro / Oiwa, Shunya / Yamasaki, Kazuhito
Extrapolating for attaining high precision solutions for fractional partial differential equations
Patrício, Fernanda Simões / Patrício, Miguel / Ramos, Higinio
Time optimal controls for fractional differential systems with Riemann-Liouville derivatives
Lian, TingTing / Fan, ZhenBin / Li, Gang
Inverses of generators of integrated fractional resolvent operator functions
Li, Miao / Pastor, Javier / Piskarev, Sergey
A variational approach for boundary value problems for impulsive fractional differential equations
Afrouzi, Ghasem A. / Hadjian, Armin
Infinitely many solutions to boundary value problem for fractional differential equations
Averna, Diego / Sciammetta, Angela / Tornatore, Elisabetta
A semi-analytic method for fractional-order ordinary differential equations: Testing results
Reutskiy, Sergiy / Fu, Zhuo-Jia
Blow-up and global existence of solutions for a time fractional diffusion equation
Li, Yaning / Zhang, Quanguo
A note on the Blaschke-Petkantschin formula, Riesz distributions, and Drury’s identity
Rubin, Boris
Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions
Liang, Yong Shun
(Selected)
Fractional viscoelastic models with non-singular kernels
Jianmin Long, Rui Xiao, Wen Chen
An equivalence between generalized Maxwell model and fractional Zener model
Rui Xiao, Hongguang Sun, Wen Chen
U. Hofer, M. Luger, R. Traxl, R. Lackner
On a general numerical scheme for the fractional plastic flow rule
Wojciech Sumelka, Marcin Nowak
Changqing Fang, Jinsong Leng, Huiyu Sun, Jianping Gu
Mario Di Paola, Vincenzo Fiore, Francesco Paolo Pinnola, Antonino Valenza
Vasily E. Tarasov
Erasmo Cataldo, Salvatore Di Lorenzo, Vincenzo Fiore, Mirko Maurici, Antonino Valenza
M. Di Paola, A. Pirrotta, A. Valenza
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Paper Highlight
Abdon Atangana
Publication information: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 505 Pages: 688-706 Published: SEP 1 2018
Abstract
We presented an analysis of evolutions equations generated by three fractional
derivatives namely the RiemannLiouville, CaputoFabrizio and the Atangana-aleanu
fractional derivatives. For each evolution equation, we presented the exact
solution for time variable and studied the semigroup principle. The Riemann-iouville
fractional operator verifies the semigroup principle but the associate evolution
equation does not. The Caputo-abrizio fractional derivative does not satisfy the
semigroup principle but surprisingly, the exact solution satisfies very well all
the principle of semigroup. However, the AtanganaBaleanu for small time is the
stretched exponential derivative, which does not satisfy the semigroup as
operators. For a large time the AtanganaBaleanu derivative is the same with
Riemann-iouville fractional derivative, thus satisfies semigroup principle as an
operator. The solution of the associated evolution equation does not satisfy the
semigroup principle as Riemann-iouville. With the connection between semigroup
theory and the Markovian processes, we found out that the Atangana-aleanu
fractional derivative has at the same time Markovian and non-Markovian
processes. We concluded that, the fractional differential operator does not need
to satisfy the semigroup properties as they portray the memory effects, which
are not always Markovian. We presented the exact solutions of some evolutions
equation using the Laplace transform. In addition to this, we presented the
numerical solution of a nonlinear equation and show that, the model with the
AtanganaBaleanu fractional derivative has random walk for small time. We also
observed that, the Mittag-Leffler function is a good filter than the exponential
and power law functions, which makes the Atangana-Baleanu fractional derivatives
powerful mathematical tools to model complex real world problems.
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Yong Zhang, Xiangnan Yu, Xicheng Li, James F.Kelly, HongGuang Sun, Chunmiao Zheng
Publication information: Advances in Water Resources Available online 27 February 2019
https://www.sciencedirect.com/science/article/pii/S0309170818309345
Abstract
Fractional-derivative models are promising tools for characterizing non-Fickian transport in heterogeneous media. Most fractional models utilize an infinite domain, although realistic problems occur on bounded domains. To quantify the impact of a finite or semi-infinite boundary on non-Fickian transport in natural geological media, this study evaluates three representative fractional advection-dispersion equations (FADEs) with absorbing or reflective boundaries. Results show that the temporal FADE (t-FADE) with absorbing/reflective boundaries has analytical solutions, the one-sided spatial FADE (s-FADE) in bounded-domains can be simulated using an Eulerian solver, and the tempered spatiotemporal FADE (st-FADE) can be efficiently solved using a fully Lagrangian approach. Further simulations reveal important impacts of absorbing/reflective boundaries on non-Fickian diffusion. First, the “local” reflective boundary mainly affects the solute dynamics near the boundary for non-local super-diffusion, while the “nonlocal” reflective boundary changes the overall pattern of non-Fickian transport in the whole domain. Second, the total mass for solutes in absorbing boundaries declines non-linearly with respect to time. Third, the mobile and immobile phase plumes tend to respond differently to the boundary because of their different transport mechanisms. Fourth, a field application shows that both the s-FADE with a negative skewness and the t-FADE can be used to quantify bounded-domain sub-diffusion for fluorescein dye transport in the Red Cedar River with a large Péclet number, although the determination of the upstream boundary position contains high uncertainty. Evaluation of the boundary impact on sub-diffusion, super-diffusion, and their mixture may improve our understanding of the nature of non-Fickian transport in bounded domains.
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