FDA Express Vol. 25, No. 3, Dec 15, 2017
All issues: http://em.hhu.edu.cn/fda/
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Institute of Soft Matter Mechanics, Hohai University
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◆ Latest SCI Journal Papers on FDA
◆ Call for papers
19th International Carpathian Control Conference
◆ Books
Hamiltonian Chaos and Fractional Dynamics
◆ Journals
Physica A: Statistical Mechanics and its Applications
◆ Paper Highlight
Comments on time-varying fractional order
◆ Patent
Chaotic series generated by discrete fractional maps
◆ 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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By: Shivanian, Elyas; Jafarabadi, Ahmad
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 325 Pages: 18-33 Published: DEC 1 2017
Integer and Fractional Self Adjoint Operator Opial type Inequalities
By: Anastassiou, George A.
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS Volume: 23 Issue: 8 Pages: 1398-1411 Published: DEC 2017
By: Ahmad, Bashir; Ntouyas, Sotiris K.; Tariboon, Jessada
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS Volume: 23 Issue: 7 Pages: 1281-1296 Published: NOV 30 2017
Conservation laws for certain time fractional nonlinear systems of partial differential equations
By: Singla, Komal; Gupta, R. K.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 53 Pages: 10-21 Published: DEC 2017
By: Ahmadian, A.; Ismail, F.; Salahshour, S.; et al.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 53 Pages: 44-64 Published: DEC 2017
Dynamics for a non-autonomous reaction diffusion model with the fractional diffusion
By: Tan, Wen; Sun, Chunyou
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume: 37 Issue: 12 Pages: 6035-6067 Published: DEC 2017
The maximum principles for fractional Laplacian equations and their applications
By: Cheng, Tingzhi; Huang, Genggeng; Li, Congming
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS Volume: 19 Issue: 6 Article Number: 1750018 Published: DEC 2017
By: Coronel-Escamilla, A.; Gomez-Aguilar, J. F.; Torres, L.; et al.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 487 Pages: 1-21 Published: DEC 1 2017
By: Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; et al.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 487 Pages: 205-214 Published: DEC 1 2017
On the uniqueness of solutions for a class of fractional differential equations
By: Zou, Yumei; He, Guoping
APPLIED MATHEMATICS LETTERS Volume: 74 Pages: 68-73 Published: DEC 2017
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Call for Papers
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19th International Carpathian Control Conference
La Contessa Castle Hotel, Szilvásvárad, Hungary
May 28-31, 2018
http://www.iccc.uni-miskolc.hu/
Description
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Books
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George M. Zaslavsky
Book Descriptioniption
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness. An understanding of the origin of randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry, and engineering.
More information on this book can be found by the following links:
Fractional Kinetics in Solids
Vladimir Uchaikin (Ulyanovsk State University, Russia), Renat Sibatov (Ulyanovsk State University, Russia)
Book Description
The standard (Markovian) transport model based on the Boltzmann equation cannot describe some non-equilibrium processes called anomalous that take place in many disordered solids. Causes of anomality lie in non-uniformly scaled (fractal) spatial heterogeneities, in which particle trajectories take cluster form. Furthermore, particles can be located in some domains of small sizes (traps) for a long time. Estimations show that path length and waiting time distributions are often characterized by heavy tails of the power law type. This behavior allows the introduction of time and space derivatives of fractional orders. Distinction of path length distribution from exponential is interpreted as a consequence of media fractality, and analogous property of waiting time distribution as a presence of memory. In this book, a novel approach using equations with derivatives of fractional orders is applied to describe anomalous transport and relaxation in disordered semiconductors, dielectrics and quantum dot systems. A relationship between the self-similarity of transport, the Levy stable limiting distributions and the kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher–Montroll and Arkhipov–Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of bipolar transport to be written down and transport in distributed dispersion systems to be described. The relationship between fractional transport equations and the generalized limit theorem reveals the probabilistic aspects of the phenomenon in which a dispersive to Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased. Recent experiments devoted to studies of transport in quantum dot arrays are discussed in the framework of dispersive transport models. The memory phenomena in systems under consideration are discussed in the analysis of fractional equations. It is shown that the approach based on the anomalous transport models and the fractional kinetic equations may be very useful in some problems that involve nano-sized systems. These are photon counting statistics of blinking single quantum dot fluorescence, relaxation of current in colloidal quantum dot arrays, and some others.
More information on this book can be found by the following links:
http://www.worldscientific.com/worldscibooks/10.1142/8185
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Journals
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(Selected)
A new generalized fractional Maxwell model of dielectric relaxation
Dan Luo, Hong-Shan Chen
Fractional physical differential equations via natural transform
Sad Rida, Anas Arafa, Ahmed Abedl-Rady, Hamdy Abdl-Rahaim
Jianqu Zhu, Weidong Jin, Feng Guo
Influence of time-fractional derivatives on the boundary layer flow of Maxwell fluids
Yasir Mahsud, Nehad Ali Shah, Dumitru Vieru
Vibrational resonance in fractional-order overdamped multistable systems
Tianqi Qin, Tianting Xie, Maokang Luo, Ke Deng
Soliton solutions for the space-time nonlinear partial differential equations with fractional-orders
Jin Hyuk Choi, Hyunsoo Kim
A microscopic study of MHD fractional inertial flow through Forchheimer medium
Muhammad Shoaib Anwar, Amer Rasheed
Synchronization of uncertain fractional-order chaotic systems via a novel adaptive controller
Runzi Luo, Haipeng Su, Yanhui Zeng
Vijay K. Yadav, Subir Das, Beer Singh Bhadauria, Ashok K. Singh, Mayank Srivastava
On certain exact solutions of diffusive predator-prey system of fractional order
Jin Hyuk Choi, Hyunsoo Kim, Rathinasamy Sakthivel
Zhi-Qi Huang, Feng Guo
On the dynamics, existence of chaos, control and synchronization of a novel complex chaotic system
K. Vishal, Saurabh K. Agrawal
[Back]
International Journal of Solids and Structure
(Selected)
A hyperelastic fractional damage material model with memory
Wojciech Sumelka, George Z. Voyiadjis
Fractional order plasticity model for granular soils subjected to monotonic triaxial compression
Yifei Sun, Yang Xiao
Fractional visco-elastic Euler–Bernoulli beam
M. Di Paola, R. Heuer, A. Pirrotta
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
Fractional order theory of thermoelasticity
Hany H. Sherief, A.M.A. El-Sayed, A.M. Abd El-Latief
Long-range cohesive interactions of non-local continuum faced by fractional calculus
Mario Di Paola, Massimiliano Zingales
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Paper Highlight
Gary W. Bohannan
Publication information: NONLINEAR DYNAMICS Volume: 90 Issue: 3 Pages: 2137-2143 Published: NOV 2017
https://link.springer.com/article/10.1007/s11071-017-3790-9
Abstract
The calculus of arbitrary order, known as the fractional calculus, allows for real- and complex-valued orders. Interest in time-varying order is growing in order to study transient behavior under varying environmental conditions. Popular forms currently in use suffer from fundamental flaws of dimensional inconsistency and predict physically implausible behaviors such as violation of causality and/or violation of conservation of energy. This article reviews some of the motivation behind the study of time-varying fractional order and makes suggestions as to how to overcome the flaws in the forms in current usage. A new fractional-order integral operator is proposed that may allow for modeling time-varying fractional-order systems in a dimensionally consistent and physically plausible manner. Possible experimental tests of the revised fractional-order model are proposed.
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Patent
Inventors: Guo-Cheng Wu, Li-Gang Zeng, Dumitru Baleanu, Xiang-Chao Shi
Chinese Patent No.: ZL 2014 1 0033835.7
Introduction
This patent generates fractional chaotic time-series in a short time, 10^5 length about 10 seconds on a student laptop. The patent overcomes long term calculation issue and keeps high sensitivity and randomicity of chaos. This patent has been successfully applied in large-scale image encryption to increase the key space.
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