FDA Express

New exact solutions for the conformable space-time fractional KdV, CDG, (2+1)-dimensional CBS and (2+1)-dimensional AKNS equations
By: Yaslan, H. C.; Girgin, A.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 13 Issue: 1 Pages: 1-8 Published: DEC 11 2019

Optimal control problem for coupled time-fractional diffusion systems with final observations
By: Bahaa, G. M.; Hamiaz, A.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 13 Issue: 1 Pages: 124-135 Published: DEC 11 2019

NEW EXACT SOLUTIONS FOR SOME FRACTIONAL ORDER DIFFERENTIAL EQUATIONS VIA IMPROVED SUB-EQUATION METHOD
By: Karaagac, Berat
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S Volume: 12 Issue: 3 Pages: 447-454 Published: JUN 2019

THE FIRST INTEGRAL METHOD FOR TWO FRACTIONAL NON-LINEAR BIOLOGICAL MODELS
By: Kolebaje, Olusola; Bonyah, Ebenezer; Mustapha, Lateef
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S Volume: 12 Issue: 3 Pages: 487-502 Published: JUN 2019

A UNIFIED FINITE DIFFERENCE CHEBYSHEV WAVELET METHOD FOR NUMERICALLY SOLVING TIME FRACTIONAL BURGERS' EQUATION
By: Oruc, Omer; Esen, Alaattin; Bulut, Fatih
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S Volume: 12 Issue: 3 Pages: 533-542 Published: JUN 2019

NUMERICAL ANALYSIS AND PATTERN FORMATION PROCESS FOR SPACE-FRACTIONAL SUPERDIFFUSIVE SYSTEMS
By: Owolabi, Kolade M.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S Volume: 12 Issue: 3 Pages: 543-566 Published: JUN 2019

HIGH-ORDER SOLVERS FOR SPACE-FRACTIONAL DIFFERENTIAL EQUATIONS WITH RIESZ DERIVATIVE
By: Owolabi, Kolade M.; Atangana, Abdon
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S Volume: 12 Issue: 3 Pages: 567-590 Published: JUN 2019

Analytical and numerical solutions of time and space fractional advection-diffusion-reaction equation
By: Jannelli, Alessandra; Ruggieri, Marianna; Speciale, Maria Paola
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 70 Pages: 89-101 Published: MAY 2019

Fractional and integer derivatives with continuously distributed lag
By: Tarasov, Vasily E.; Tarasova, Svetlana S.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 70 Pages: 125-169 Published: MAY 2019

Electrical transport properties and fractional dynamics of twist-bend nematic liquid crystal phase
By: Ribeiro de Almeida, R. R.; Evangelista, L. R.; Lenzi, K.; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 70 Pages: 248-256 Published: MAY 2019

On power law scaling dynamics for time-fractional phase field models during coarsening
By: Zhao, Jia; Chen, Lizhen; Wang, Hong
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 70 Pages: 257-270 Published: MAY 2019

Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations
By: Garrappa, Roberto
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 70 Pages: 302-306 Published: MAY 2019

Fractional-order modeling of a diode
By: Tenreiro Machado, J. A.; Lopes, Antonio M.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 70 Pages: 343-353 Published: MAY 2019

Finite difference/finite element method for a novel 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains
By: Feng, Libo; Liu, Fawang; Turner, Ian
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 70 Pages: 354-371 Published: MAY 2019

Fractional calculus via Laplace transform and its application in relaxation processes
By: Capelas de Oliveira, E.; Jarosz, S.; Vaz, J., Jr.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 69 Pages: 58-72 Published: APR 2019

On an accurate discretization of a variable-order fractional reaction-diffusion equation
By: Hajipour, Mojtaba; Jajarmi, Amin; Baleanu, Dumitru; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 69 Pages: 119-133 Published: APR 2019

Emergence of death islands in fractional-order oscillators via delayed coupling
By: Xiao, Rui; Sun, Zhongkui; Yang, Xiaoli; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 69 Pages: 168-175 Published: APR 2019

On the series representation of nabla discrete fractional calculus
By: Wei, Yiheng; Gao, Qing; Liu, Da-Yan; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 69 Pages: 198-218 Published: APR 2019

Numerical solution of Caputo fractional differential equations with infinity memory effect at initial condition
By: Mendes, Eduardo M. A. M.; Salgado, Gustavo H. O.; Aguirre, Luis A.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 69 Pages: 237-247 Published: APR 2019

Stable evaluations of fractional derivative of the Muntz-Legendre polynomials and application to fractional differential equations
By: Erfani, S.; Babolian, E.; Javadi, S.; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 348 Pages: 70-88 Published: MAR 1 2019

Analytical solution of fractional variable order differential equations
By: Malesza, W.; Macias, M.; Sierociuk, D.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 348 Pages: 214-236 Published: MAR 1 2019

Weakly singular Gronwall inequalities and applications to fractional differential equations
By: Webb, J. R. L.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 471 Issue: 1-2 Pages: 692-711 Published: MAR 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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Fractional Dynamics, Anomalous Transport and Plasma Science

( Editors: Skiadas, Christos H. )

Details: https://www.springer.com/cn/book/9783030044824

Introduction

This book collects interrelated lectures on fractal dynamics, anomalous transport and various historical and modern aspects of plasma sciences and technology.

The origins of plasma science in connection to electricity and electric charges and devices leading to arc plasma are explored in the first contribution by Jean-Marc Ginoux and Thomas Cuff. The second important historic connection with plasmas was magnetism and the magnetron. Victor J. Law and Denis P. Dowling, in the second contribution, review the history of the magnetron based on the development of thermionic diode valves and related devices. In the third chapter, Christos H Skiadas and Charilaos Skiadas present and apply diffusion theory and solution strategies to a number of stochastic processes of interest. Anomalous diffusion by the fractional Fokker-Planck equation and Lévy stable processes are studied by Johan Anderson and Sara Moradi in the fourth contribution. They consider the motion of charged particles in a 3-dimensional magnetic field in the presence of linear friction and of a stochastic electric field. Analysis of low-frequency instabilities in a low-temperature magnetized plasma is presented by Dan-Gheorghe Dimitriu, Maricel Agop in the fifth chapter. The authors refer to experimental results of the Innsbruck Q-machine and provide an analytical formulation of the related theory. In chapter six, Stefan Irimiciuc, Dan-Gheorghe Dimitriu, Maricel Agop propose a theoretical model to explain the dynamics of charged particles in a plasma discharge with a strong flux of electrons from one plasma structure to another. The theory and applications of fractional derivatives in many-particle disordered large systems are explored by Z.Z. Alisultanov, A.M. Agalarov, A.A. Potapov, G.B. Ragimkhanov. In chapter eight, Maricel Agop, Alina Gavrilut¸ and Gabriel Crumpei explore the motion of physical systems that take place on continuous but non-differentiable curves (fractal curves). Finally in the last chapter S.L. Cherkas and V.L. Kalashnikov consider the perturbations of a plasma consisting of photons, baryons, and electrons in a linearly expanding (Milne-like) universe taking into account the metric tensor and vacuum perturbations.

Chapters

-From Branly Coherer to Chua Memristor

-Magnetron Modes and the Chimera State

-The Fokker-Planck Equation and the First Exit Time Problem. A Fractional Second Order Approximation

-Anomalous Diffusion by the Fractional Fokker-Planck Equation and Lévy Stable Processes

-Analysis of Low-Frequency Instabilities in Low-Temperature Magnetized Plasma

-Theoretical Modeling of the Interaction Between Two Complex Space Charge Structures in Low-Temperature Plasma

-Some Applications of Fractional Derivatives in Many-Particle Disordered Large Systems

-Similarities Between Dynamics at Atomic and Cosmological Scales

-Plasma Perturbations and Cosmic Microwave Background Anisotropy in the Linearly Expanding Milne-Like Universe

The Contents is available at: https://www.springer.com/cn/book/9783030044824

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Journals
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Physica A: Statistical Mechanics and its Applications

(Selected)

Revisiting fractional Gaussian noise

Ming Li, Xichao Sun, Xi Xiao

Fractional conformable derivatives of Liouville–Caputo type with low-fractionality

V. F. Morales-Delgado, J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, M. A. Taneco-Hernández

The fractional space–time radial diffusion equation in terms of the Fox’s H-function

F. S. Costa, D. S. Oliveira, F. G. Rodrigues, E. C. de Oliveira

Analytical solution of the space–time fractional hyperdiffusion equation

Ashraf M. Tawfik, Horst Fichtner, A. Elhanbaly, Reinhard Schlickeiser

Modified fractional logistic equation

Mirko D’Ovidio, Paola Loreti, Sima Sarv Ahrabi

Chaotic analysis and adaptive synchronization for a class of fractional order financial system

Xiao-Li Gong, Xi-Hua Liu, Xiong Xiong

An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein–Gordon equations in fluid mechanics

E. Hashemizadeh, A. Ebrahimzadeh

A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics

Dong Lei, Yingjie Liang, Rui Xiao

Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

Mustafa Inc, Abdullahi Yusuf, Aliyu Isa Aliyu, Dumitru Baleanu

Solutions of fractional logistic equations by Euler’s numbers

Mirko D’Ovidio, Paola Loreti

Multivariate multiscale fractional order weighted permutation entropy of nonlinear time series

Shijian Chen, Pengjian Shang, Yue Wu

Market efficiency of Baltic stock markets: A fractional integration approach

Luis A. Gil-Alana, Rangan Gupta, Olanrewaju I. Shittu, OlaOluwa S. Yaya

Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties

Abdon Atangana

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Construction and Building Materials

(Selected)

Study of the mechanical behavior of asphalt mixtures using fractional rheology to model their viscoelasticity

M. Lagos-Varas, D. Movilla-Quesada, J. P. Arenas, A. C. Raposeiras, J. Maturana

Introducing a stress-dependent fractional nonlinear viscoelastic model for modified asphalt binders

Pouria Hajikarimi, Fereidoon Moghadas Nejad, Ali Khodaii, Ellie H. Fini

Fractional linear viscoelastic constitutive relations of anhydride-cured thermosetting rubber-like epoxy asphalt binders

Qiang Wu, Chong Wang, Rui Liang, Yongchang Liu, Yang Kang

Experimental validation of a fractional model for creep/recovery testing of asphalt mixtures

C. Celauro, C. Fecarotti, A. Pirrotta, A. C. Collop

Implementing fractional viscoelastic model to evaluate low temperature characteristics of crumb rubber and gilsonite modified asphalt binders

Pouria Hajikarimi, Sassan Aflaki, Alireza Sadat Hoseini

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Paper Highlight

An efficient numerical algorithm for the fractional Drinfeld-Sokolov-Wilson equation

Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; Rathore, Sushila

Publication information: APPLIED MATHEMATICS AND COMPUTATION Volume: 335 Pages: 12-24 Published: OCT 15 2018

http://apps.webofknowledge.com/full_record.do?product=UA&search_mode=GeneralSearch&qid=2&SID=5DsEPkL2dmUKCtXj58u&page=1&doc=1&cacheurlFromRightClick=no

Abstract

The fundamental purpose of the present paper is to apply an effective numerical algorithm based on the mixture of homotopy analysis technique, Sumudu transform approach and homotopy polynomials to obtain the approximate solution of a nonlinear fractional Drinfeld-Sokolov-Wilson equation. The nonlinear Drinfeld-Sokolov-Wilson equation naturally occurs in dispersive water waves. The uniqueness and convergence analysis are shown for the suggested technique. The convergence of the solution is fixed and managed by auxiliary parameter h. The numerical results are shown graphically. Results obtained by the application of the technique disclose that the suggested scheme is very accurate, flexible, effective and simple to use.

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Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media

Liang, Yingjie; Chen, Wen; Xu, Wei; Sun, HongGuang

Publication information: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 70 Pages: 384-393 Published: MAY 2019

http://apps.webofknowledge.com/full_record.do?product=UA&search_mode=GeneralSearch&qid=5&SID=5DsEPkL2dmUKCtXj58u&page=1&doc=1&cacheurlFromRightClick=no

Abstract

Many theoretical and experimental results show that solute transport in heterogeneous porous media exhibits multi-scaling behaviors. To describe such non-Fickian diffusion, this work provides a distributed order Hausdorff diffusion model to describe the tracer transport in porous media. This model is proved to be equivalent with the diffusion equation model with a nonlinear time dependent diffusion coefficient. In conjunction with the structural derivative, its mean squared displacement (MSD) of the tracer particles is explicitly derived as a dilogarithm function when the weight function of the order distribution is a linear function of the derivative order p(alpha)= 2c alpha. This model can capture both accelerating and decelerating anomalous and ultraslow diffusions by varying the weight parameter c. In this study, the tracer transport in water-filled pore spaces of two-dimensional Euclidean is demonstrated as a decelerating sub-diffusion, and can well be described by the distributed order Hausdorff diffusion model with c = 0.58. While the Hausdorff diffusion model with alpha = 0.97 can accurately fit the sub-diffusion experimental data of the tracer transport in the pore-solid prefractal porous media.

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