Fractional Dynamics and Control
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1 Fractional Dynamics and Control
2
3 Dumitru Baleanu JoséAntónio Tenreiro Machado Albert C. J. Luo Editors Fractional Dynamics and Control 123
4 Editors Dumitru Baleanu Mathematics and Computer Sciences Faculty of Art and Sciences Cankaya University Ankara Turkey José António Tenreiro Machado Department of Electrical Engineering Polytechnic Institute of Porto Institute of Engineering Rua Dr António Bernadino Almeida Porto Portugal Albert C. J. Luo Mechanical and Industrial Engineering School of Engineering Southern Illinois University Room: EB2064 Edwardsville USA ISBN e-isbn DOI / Springer New York Dordrecht Heidelberg London Library of Congress Control Number: Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (
5 Preface Fractional calculus is as old as the classical one and it started to be intensively studied and applied in many branches of science and engineering. The fractional dynamics is growing faster during the few decades together with the fractional control theory which certified the fractional calculus as being a fundamental tool in describing the dynamics of complex systems. This book is based on the 3rd conference on Nonlinear Science and Complexity (NSC), Ankara, Turkey, July 27 31, Due to the impact of topics on a very wide spectrum of problems in science and engineering, this conference provided a place to exchange recent developments, discoveries and progresses on nonlinear science and complexity. This conference is the continuation of the first 2006 Conference on Nonlinear Science and Complexity, Beijing, China, and the second 2008 conference on Nonlinear Science and Complexity held in Porto, Portugal. This book it is entitled Fractional Dynamics and Control and it collects the recent development in nonlinear dynamics, nonlinear vibration and control. The aim of this book provides a fast exchange idea in nonlinear dynamical systems and control. One can learn the recent developments, including analytical, numerical and experimental results in such area. The editors hope that this collection of papers may be fruitful for scholars, researchers and advanced technical members of industrial laboratory facilities, for developing new tools and products. The editors thank to the Rector and to the President of the Board of Trustee of Cankaya University as well as to the Scientific and Technological Research Council of Turkey for the financial support needed to hold the discussions and debates. Dumitru Baleanu José António Tenreiro Machado Albert C. J. Luo v
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7 Contents Part I Fractional Control 1 A Formulation and Numerical Scheme for Fractional Optimal Control of Cylindrical Structures Subjected to General Initial Conditions... 3 Md. Mehedi Hasan, X.W. Tangpong, and O.P. Agrawal 2 Neural Network-Assisted PI D Control Mehmet Önder Efe 3 Application of Backstepping Control Technique to Fractional Order Dynamic Systems Mehmet Önder Efe 4 Parameter Tuning of a Fractional-Order PI Controller Using the ITAE Criteria Badreddine Boudjehem and Djalil Boudjehem 5 A Fractional Model Predictive Control for Fractional Order Systems Djalil Boudjehem and Badreddine Boudjehem 6 A Note on the Sequential Linear Fractional Dynamical Systems from the Control System Viewpoint and L 2 -Theory Abolhassan Razminia, Vahid Johari Majd, and Ahmad Feiz Dizaji 7 Stabilization of Fractional Order Unified Chaotic Systems via Linear State Feedback Controller E.G. Razmjou, A. Ranjbar, Z. Rahmani, R. Ghaderi, and S. Momani vii
8 viii Contents Part II Fractional Variational Principles and Fractional Differential Equations 8 Fractional Variational Calculus for Non-differentiable Functions Agnieszka B. Malinowska 9 Fractional Euler Lagrange Differential Equations via Caputo Derivatives Ricardo Almeida, Agnieszka B. Malinowska, and Delfim F.M. Torres 10 Strict Stability of Fractional Perturbed Systems in Terms of Two Measures Coşkun Yakar, Mustafa Bayram Gücen, and Muhammed Çiçek 11 Initial Time Difference Strict Stability of Fractional Dynamic Systems Coşkun Yakar and Mustafa Bayram Gücen 12 A Fractional Order Dynamical Trajectory Approach for Optimization Problem with HPM Fırat Evirgen and Necati Özdemir Part III Fractional Calculus in Mathematics and Physics 13 On the Hadamard Type Fractional Differential System Ziqing Gong, Deliang Qian, Changpin Li, and Peng Guo 14 Robust Synchronization and Parameter Identification of a Unified Fractional-Order Chaotic System E.G. Razmjou, A. Ranjbar, Z. Rahmani, and R. Ghaderi 15 Fractional Cauchy Problems on Bounded Domains: Survey of Recent Results Erkan Nane 16 Fractional Analogous Models in Mechanics and Gravity Theories Dumitru Baleanu and Sergiu I. Vacaru 17 Schrödinger Equation in Fractional Space Sami I. Muslih and Om P. Agrawal 18 Solutions of Wave Equation in Fractional Dimensional Space Sami I. Muslih and Om P. Agrawal 19 Fractional Exact Solutions and Solitons in Gravity Dumitru Baleanu and Sergiu I. Vacaru
9 Contents ix Part IV Fractional Order Modeling 20 Front Propagation in an Autocatalytic Reaction-Subdiffusion System Igor M. Sokolov and Daniela Froemberg 21 Numerical Solution of a Two-Dimensional Anomalous Diffusion Problem Necati Özdemir and Derya Avcı 22 Analyzing Anomalous Diffusion in NMR Using a Distribution of Rate Constants R.L. Magin, Y.Z. Rawash, and M.N. Berberan-Santos 23 Using Fractional Derivatives to Generalize the Hodgkin Huxley Model Hany H. Sherief, A.M.A. El-Sayed, S.H. Behiry, and W.E. Raslan 24 An Application of Fractional Calculus to Dielectric Relaxation Processes M.S. Çavuş and S. Bozdemir 25 Fractional Wave Equation for Dielectric Medium with Havriliak Negami Response R.T. Sibatov, V.V. Uchaikin, and D.V. Uchaikin Index
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