FDA Express Vol. 7, No. 3, May 15, 2013
Editors: http://em.hhu.edu.cn/fda/Editors.htm Institute of Soft Matter Mechanics, Hohai University For contribution: [email protected], [email protected] For subscription: http://em.hhu.edu.cn/fda/subscription.htm PDF Download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol7_No3_2013.pdf
◆ Latest SCI Journal Papers on FDA
(Searched on 14 May 2013)
◆ Conferences
The International Conference "MATHEMATICAL METHODS IN ENGINEERING"
◆ Books
A Tale of Two Fractals
◆ Journals
Communications in Nonlinear Science and Numerical Simulation
Chaos
◆ Paper Highlight
Applications of fractional calculus to the theory of viscoelasticity
Analysis of four-parameter fractional derivative model of real solid materials
◆ Websites of Interest
Fractional Calculus & Applied Analysis, Volume 16, No 1, 2013
======Latest SCI Journal Papers on FDA
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(Searched on 14 May 2013)
Title: Some existence results on nonlinear fractional differential equations Author(s): Baleanu, Dumitru; Rezapour, Shahram; Mohammadi, Hakimeh Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120144 DOI: 10.1098/rsta.2012.0144 Published: MAY 13 2013
Title: Fractional-order variational optical flow model for motion estimation Author(s): Chen, Dali; Sheng, Hu; Chen, YangQuan; et al. Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120148 DOI: 10.1098/rsta.2012.0148 Published: MAY 13 2013
Title: A high-speed algorithm for computation of fractional differentiation and fractional integration Author(s): Fukunaga, Masataka; Shimizu, Nobuyuki Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120152 DOI: 10.1098/rsta.2012.0152 Published: MAY 13 2013
Title: On reflection symmetry and its application to the Euler-Lagrange equations in fractional mechanics Author(s): Klimek, Malgorzata Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120145 DOI: 10.1098/rsta.2012.0145 Published: MAY 13 2013
Title: Fractional calculus and its applications Author(s): Li, Changpin; Chen, YangQuan; Kurths, Juergen Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20130037 DOI: 10.1098/rsta.2013.0037 Published: MAY 13 2013
Title: Equivalent system for a multiple-rational-order fractional differential system Author(s): Li, Changpin; Zhang, Fengrong; Kurths, Juergen; et al. Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120156 DOI: 10.1098/rsta.2012.0156 Published: MAY 13 2013
Title: Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations Author(s): Lorenzo, C. F.; Hartley, T. T.; Malti, R. Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120151 DOI: 10.1098/rsta.2012.0151 Published: MAY 13 2013
Title: Matrix approach to discrete fractional calculus III: non-equidistant grids, variable step length and distributed orders Author(s): Podlubny, Igor; Skovranek, Tomas; Vinagre Jara, Blas M.; et al. Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120153 DOI: 10.1098/rsta.2012.0153 Published: MAY 13 2013
Title: Modelling heat transfer in heterogeneous media using fractional calculus Author(s): Sierociuk, Dominik; Dzielinski, Andrzej; Sarwas, Grzegorz; et al. Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120146 DOI: 10.1098/rsta.2012.0146 Published: MAY 13 2013
Title: A semi-discrete finite element method for a class of time-fractional diffusion equations Author(s): Sun, HongGuang; Chen, Wen; Sze, K. Y. Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120268 DOI: 10.1098/rsta.2012.0268 Published: MAY 13 2013
Title: Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation Author(s): Yu, Qiang; Liu, Fawang; Turner, Ian; et al. Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120150 DOI: 10.1098/rsta.2012.0150 Published: MAY 13 2013
Title: Chaos synchronization in fractional differential systems Author(s): Zhang, Fengrong; Chen, Guanrong; Li, Changpin; et al. Source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume: 371 Issue: 1990 Special Issue: SI Article Number: 20120155 DOI: 10.1098/rsta.2012.0155 Published: MAY 13 2013
Title: A De Giorgi-Nash type theorem for time fractional diffusion equations Author(s): Zacher, Rico Source: MATHEMATISCHE ANNALEN Volume: 356 Issue: 1 Pages: 99-146 DOI: 10.1007/s00208-012-0834-9 Published: MAY 2013
Title: Application of the nonlocal Darcy law to the propagation of nonlinear thermoelastic waves in fluid saturated porous media Author(s): Garra, R.; Salusti, E. Source: PHYSICA D-NONLINEAR PHENOMENA Volume: 250 Pages: 52-57 DOI: 10.1016/j.physd.2013.01.014 Published: MAY 1 2013
Title: Laplace-Transform Based Inversion Method for Fractional Dispersion Author(s): Ouloin, M.; Maryshev, B.; Joelson, M.; et al. Source: TRANSPORT IN POROUS MEDIA Volume: 98 Issue: 1 Pages: 1-14 DOI: 10.1007/s11242-012-0104-z Published: MAY 2013
Title: Active disturbance rejection control for fractional-order system. Author(s): Li, Mingda; Li, Donghai; Wang, Jing; et al. Source: ISA transactions Volume: 52 Issue: 3 Pages: 365-74 DOI: 10.1016/j.isatra.2013.01.001 Published: 2013-May (Epub 2013 Feb 08)
Title: A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations Author(s): Wang, Hong; Du, Ning Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 240 Pages: 49-57 DOI: 10.1016/j.jcp.2012.07.045 Published: MAY 1 2013
Title: Deformation of roots of polynomials via fractional derivatives Author(s): Galligo, Andre Source: JOURNAL OF SYMBOLIC COMPUTATION Volume: 52 Special Issue: SI Pages: 35-50 DOI: 10.1016/j.jsc.2012.05.011 Published: MAY 2013
Title: Unique continuation property for the anomalous diffusion and its application Author(s): Cheng, Jin; Lin, Ching-Lung; Nakamura, Gen Source: JOURNAL OF DIFFERENTIAL EQUATIONS Volume: 254 Issue: 9 Pages: 3715-3728 DOI: 10.1016/j.jde.2013.01.039 Published: MAY 1 2013
Title: A Caputo Fractional Order Boundary Value Problem with Integral Boundary Conditions Author(s): Babakhani, Azizollah; Abdeljawad, Thabet Source: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS Volume: 15 Issue: 4 Pages: 753-763 Published: MAY 2013
Title: On chaos control and synchronization of the commensurate fractional order Liu system Author(s): Hegazi, A. S.; Ahmed, E.; Matouk, A. E. Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 5 Pages: 1193-1202 DOI: 10.1016/j.cnsns.2012.09.026 Published: MAY 2013
Title: Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW Author(s): Zhu, Li; Fan, Qibin Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 5 Pages: 1203-1213 DOI: 10.1016/j.cnsns.2012.09.024 Published: MAY 2013
Title: Numerical approach for solving fractional relaxation-oscillation equation Author(s): Gulsu, Mustafa; Ozturk, Yalcin; Anapali, Ayse Source: APPLIED MATHEMATICAL MODELLING Volume: 37 Issue: 8 Pages: 5927-5937 DOI: 10.1016/j.apm.2012.12.015 Published: APR 15 2013
Title: Numerical solution of the fractional-order Vallis systems using multi-step differential transformation method Author(s): Merdan, Mehmet Source: APPLIED MATHEMATICAL MODELLING Volume: 37 Issue: 8 Pages: 6025-6036 DOI: 10.1016/j.apm.2012.11.007 Published: APR 15 2013
Title: Fractional order iterative functional differential equations with parameter Author(s): Wang, JinRong; Feckan, Michal; Zhou, Yong Source: APPLIED MATHEMATICAL MODELLING Volume: 37 Issue: 8 Pages: 6055-6067 DOI: 10.1016/j.apm.2012.12.011 Published: APR 15 2013
Title: Parameter and differentiation order estimation in fractional models Author(s): Victor, Stephane; Malti, Rachid; Garnier, Hugues; et al. Source: AUTOMATICA Volume: 49 Issue: 4 Pages: 926-935 DOI: 10.1016/j.automatica.2013.01.026 Published: APR 2013
Title: A numerical method for solving a fractional partial differential equation through converting it into an NLP problem Author(s): Ghandehari, Mohammad Ali Mohebbi; Ranjbar, Mojtaba Source: COMPUTERS & MATHEMATICS WITH APPLICATIONS Volume: 65 Issue: 7 Pages: 975-982 DOI: 10.1016/j.camwa.2013.01.003 Published: APR 2013
Title: Adaptive control and synchronization of a fractional-order chaotic system Author(s): Li, Chunlai; Tong, Yaonan Source: PRAMANA-JOURNAL OF PHYSICS Volume: 80 Issue: 4 Pages: 583-592 DOI: 10.1007/s12043-012-0500-5 Published: APR 2013
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Conferences
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ The International Conference "MATHEMATICAL METHODS IN ENGINEERING"
---- The Institute of Engineering of the Polytechnic of Porto, Portugal, July 22-26, 2013
http://www.dma.isep.ipp.pt/mme2013/
Scope The International Conference "MATHEMATICAL METHODS IN ENGINEERING" will be held in the Institute of Engineering of the Polytechnic of Porto, Portugal, July 22-26, 2013. The aim of this conference is to bring together scientists and engineers to present and discuss some recent developments in the area of Mathematical Methods in Engineering. The conference is designed to maximize the involvement of all participants and will present the state of the art research and the latest achievements.
Symp-04 Title: Fractional calculus and its applications
Organizers: Dumitru Baleanu, Cankaya University, Ankara,Turkey - [email protected] Xiao-Jun Yang, China University of Mining & Technology, Xuzhou, P. R. China - [email protected]
Abstract: The theory and applications of fractional differential equations are gaining relevance since they are used in the modeling of different processes in various branches in science and engineering. The aim of this symposium is to bring together researchers from various disciplines in order to debate the open problems of the fractional calculus and its applications.
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Books
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A Tale of Two Fractals
A.A. Kirillov
Book Description Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.
Contents Part I The Sierpinski Gasket 1 Definitions and General Properties 2 The Laplace Operator on the Sierpinski Gasket 3 Harmonic Functions on the Sierpinski Gasket Part II The Apollonian Gasket 4 Circles and Disks on Spheres 5 Definitions of the Apollonian Gasket 6 Arithmetic Properties of Apollonian Gaskets 7 Geometric and Group- Theoretic Approach 8 Multi-dimensional Apollonian Gaskets Bibliography
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Journals
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Communications in Nonlinear Science and Numerical Simulation
Volume18, Issue10
Regular Articles
Mathematical Methods
Conservation laws and exact solutions for nonlinear diffusion in anisotropic media Elena D. Avdonina, Nail H. Ibragimov
Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives Yuji Liu
Replication of chaos M.U. Akhmet, M.O. Fen Different kinds of exact solutions with two-loop character of the two-component short pulse equations of the first kind Weiguo Rui
Analytical solutions to detect the scheme dispersion for the coupled nonlinear equations A.V. Porubov, D. Bouche, G. Bonnaud
Nonlinear Fluids
Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins Partner L. Ndlovu, Raseelo J. Moitsheki
Analytical studies on the instabilities of heterogeneous intelligent traffic flow D. Ngoduy
Chaos and Complexity
-random attractors and random equilibria for stochastic reaction–diffusion equations with multiplicative noises Wenqiang Zhao
A scoring mechanism for the rank aggregation of network robustness Alireza Yazdani, Leonardo Dueñas-Osorio, Qilin Li
Nonlinear system identification employing automatic differentiation Jan Schumann-Bischoff, Stefan Luther, Ulrich Parlitz
Synchronization
Asymptotical synchronization for chaotic Lur’e systems using sampled-data control Chuan-Ke Zhang, L. Jiang, Yong He, Q.H. Wu, Min Wu
Group synchronization in complex dynamical networks with different types of oscillators and adaptive coupling schemes Zhen Jia, Xinchu Fu, Guangming Deng, Kezan Li
Multivalued synchronization by Poincaré coupling L nta n- arc a ampos-Cantón, R. Femat, I. Campos-Cantón, M. Bonilla-Marín
Effect of spatial distribution on the synchronization in rings of coupled oscillators Hongjing Ma, Weiqing Liu, Ye Wu, Yixian Yang, Jinghua Xiao
Control of synchronization and spiking regularity by heterogenous aperiodic high-frequency signal in coupled excitable systems Ying-Mei Qin, Jiang Wang, Cong Men, Wai-Lok Chan, Xi-Le Wei, Bin Deng Self-synchronization of coupled chaotic FitzHugh–Nagumo systems with unreliable communication links Dedong Yang
Nonlinear Dynamical Systems
Homogeneous feedback design of differential inclusions based on control Lyapunov functions Junfeng Zhang, Zhengzhi Han, Jun Huang
A new lattice model of traffic flow with the consideration of individual difference of anticipation driving behavior Guanghan Peng
Dynamics modelling and Hybrid Suppression Control of space robots performing cooperative object manipulation P. Zarafshan, S. Ali A. Moosavian
An asymmetric image cryptosystem based on the adaptive synchronization of an uncertain unified chaotic system and a cellular neural network Chao-Jung Cheng, Chi-Bin Cheng
Instability of cooperative adaptive cruise control traffic flow: A macroscopic approach D. Ngoduy
Suprathreshold stochastic resonance in multilevel threshold system driven by multiplicative and additive noises Yongfeng Guo, Jianguo Tan
The fractional supertrace identity and its application to the super Jaulent–Miodek hierarchy Hui Wang, Tie-Cheng Xia
Application of three controls optimally in a vector-borne disease – a mathematical study T.K. Kar, Soovoojeet Jana
An adaptive sliding mode backstepping control for the mobile manipulator with nonholonomic constraints Naijian Chen, Fangzhen Song, Guoping Li, Xuan Sun, Changsheng Ai
Nonlinear Vibration
Fractional derivative and time delay damper characteristics in Duffing–van der Pol oscillators A.Y.T. Leung, Zhongjin Guo, H.X. Yang
Effect of contact stiffness modulation in contact-mode AFM under subharmonic excitation Ilham Kirrou, Mohamed Belhaq Nonlinear dynamics and bifurcations in external feedback control of microcantilevers in atomic force microscopy Kazuyuki Yagasaki
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Chaos
Volume 23, Issue 2
Regular Articles
Attracting and repelling Lagrangian coherent structures from a single computation Mohammad Farazmand and George Haller
Intermittency in relation with 1/f noise and stochastic differential equations J. Ruseckas and B. Kaulakys
Beyond long memory in heart rate variability: An approach based on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity Argentina Leite, Ana Paula Rocha, and Maria Eduarda Silva
Bifurcations in a low-order nonlinear model of tropical Pacific sea surface temperatures derived from observational data Mei Hong, Ren Zhang, Hui-Zan Wang, Jing-jing Ge, and Ao-Da Pan
Characterization of multiscroll attractors using Lyapunov exponents and Lagrangian coherent structures Filipe I. Fazanaro, Diogo C. Soriano, Ricardo Suyama, Romis Attux, Marconi K. Madrid, and José Raimundo de Oliveira
Child allowances, fertility, and chaotic dynamics Hung-Ju Chen and Ming-Chia Li
Effective suppressibility of chaos Álvaro G. López, Jesús M. Seoane, and Miguel A. F. Sanjuán
Robust global synchronization of two complex dynamical networks Mohammad Mostafa Asheghan and Joaquín Míguez
Eigenstates and instabilities of chains with embedded defects J. D'Ambroise, P. G. Kevrekidis, and S. Lepri Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency Seiji Uenohara, Takahito Mitsui, Yoshito Hirata, Takashi Morie, Yoshihiko Horio, and Kazuyuki Aihara
Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram Mathew P. Dafilis, Federico Frascoli, Peter J. Cadusch, and David T. J. Liley
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Paper Highlight
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Applications of fractional calculus to the theory of viscoelasticity
R. C. Koeller
Publication information: R. C. Koeller, Applications of fractional calculus to the theory of viscoelasticity, Journal of Applied Mechanics, 1984, 51(2): 299-307. http://cat.inist.fr/?aModele=afficheN&cpsidt=9670707
Abstract The connection between the fractional calculus and the theory of Abel's integral equation is shown for materials with memory. Expressions for creep and relaxation functions, in terms of the Mittag-Leffler function that depends on the fractional derivative parameter , are obtained. These creep and relaxation functions allow for significant creep or relaxation to occur over many decade intervals when the memory parameter is in the range of 0.05-0.35. It is shown that the fractional calculus constitutive equation allows for a continuous transition from the solid state to the fluid state when the memory parameter varies from zero to one.
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Analysis of four-parameter fractional derivative model of real solid materials
T. Pritz
Publication information: T. Pritz, Analysis of four-parameter fractional derivative model of real solid materials. Journal of Sound and Vibration, 195(1), 1996, Pages 103-115. http://www.sciencedirect.com/science/article/pii/S0022460X9690406X Abstract The introduction of fractional derivatives into the constitutive equation of the differential operator type of linear solid materials has led to the development of the so-called fractional derivative models. One of these models, characterized by four parameters, has been found usable for describing the variation of dynamics elastic and damping properties in a wide frequency range, provided that there is only one loss peak. In this paper this four-parameter model is theoretically analyzed. The effect of the parameters on the frequency curves is demonstrated, and it is shown that there is a strict relation between the dispersion of the dynamic modulus, the loss peak and the slope of the frequency curves. The half-value bandwidth of the loss modulus frequency curve is investigated, and conditions are developed to establish the applicability of the model for a class of materials. Moreover, it is shown that the model can be used to predict the frequency dependences of dynamic properties for a wide range even if measurements are made in only a narrow frequency range around the loss peak.
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The End of This Issue
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