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Fractional Dynamics and Control

  • Book
  • © 2012

Overview

Editors:
  1. Dumitru Baleanu

    1. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

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  2. José António Tenreiro Machado

    1. Institute of Engineering, Department of Electrical Engineering, Polytechnic Institute of Porto, Porto, Portugal

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    You can also search for this editor in PubMed   Google Scholar

  3. Albert C. J. Luo

    1. Edwardsville, School of Engineering, Southern Illinois University, Edwardsville, USA

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  • Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues
  • Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation
  • Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics
  • Develops new methods for control and synchronization of factional dynamical systems

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-ix
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  2. Fractional Control

    1. Front Matter

      Pages 1-1
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  3. FRACTIONAL CONTROL

    1. A Formulation and Numerical Scheme for Fractional Optimal Control of Cylindrical Structures Subjected to General Initial Conditions

      • Md. Mehedi Hasan, X. W. Tangpong, O. P. Agrawal
      Pages 3-17

    2. Neural Network-Assisted PIλDμ Control

      • Mehmet Önder Efe
      Pages 19-31

    3. Application of Backstepping Control Technique to Fractional Order Dynamic Systems

      • Mehmet Önder Efe
      Pages 33-47

    4. Parameter Tuning of a Fractional-Order PI Controller Using the ITAE Criteria

      • Badreddine Boudjehem, Djalil Boudjehem
      Pages 49-57

    5. A Fractional Model Predictive Control for Fractional Order Systems

      • Djalil Boudjehem, Badreddine Boudjehem
      Pages 59-71

    6. A Note on the Sequential Linear Fractional Dynamical Systems from the Control System Viewpoint and L 2 -Theory

      • Abolhassan Razminia, Vahid Johari Majd, Ahmad Feiz Dizaji
      Pages 73-83

    7. Stabilization of Fractional Order Unified Chaotic Systems via Linear State Feedback Controller

      • E. G. Razmjou, A. Ranjbar, Z. Rahmani, R. Ghaderi, S. Momani
      Pages 85-94

  4. Fractional Variational Principles and Fractional Differential Equations

    1. Front Matter

      Pages 95-95
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  5. FRACTIONAL VARIATIONAL PRINCIPLES AND FRACTIONAL DIFFERENTIAL EQUATIONS

    1. Fractional Variational Calculus for Non-differentiable Functions

      • Agnieszka B. Malinowska
      Pages 97-108

    2. Fractional Euler–Lagrange Differential Equations via Caputo Derivatives

      • Ricardo Almeida, Agnieszka B. Malinowska, Delfim F. M. Torres
      Pages 109-118

    3. Strict Stability of Fractional Perturbed Systems in Terms of Two Measures

      • Coşkun Yakar, Mustafa Bayram Gücen, Muhammed Çiçek
      Pages 119-132

    4. Initial Time Difference Strict Stability of Fractional Dynamic Systems

      • Coşkun Yakar, Mustafa Bayram Gücen
      Pages 133-144

    5. A Fractional Order Dynamical Trajectory Approach for Optimization Problem with HPM

      • Firat Evirgen, Necati Özdemir
      Pages 145-155

  6. Fractional Calculus in Mathematics and Physics

    1. Front Matter

      Pages 157-157
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  7. FRACTIONAL CALCULUS IN MATHEMATICS AND PHYSICS

    1. On the Hadamard Type Fractional Differential System

      • Ziqing Gong, Deliang Qian, Changpin Li, Peng Guo
      Pages 159-171

    2. Robust Synchronization and Parameter Identification of a Unified Fractional-Order Chaotic System

      • E. G. Razmjou, A. Ranjbar, Z. Rahmani, R. Ghaderi
      Pages 173-184

    3. Fractional Cauchy Problems on Bounded Domains: Survey of Recent Results

      • Erkan Nane
      Pages 185-198

    4. Fractional Analogous Models in Mechanics and Gravity Theories

      • Dumitru Baleanu, Sergiu I. Vacaru
      Pages 199-207
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Keywords

About this book

Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.

Editors and Affiliations

  • Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  • Institute of Engineering, Department of Electrical Engineering, Polytechnic Institute of Porto, Porto, Portugal

    José António Tenreiro Machado

  • Edwardsville, School of Engineering, Southern Illinois University, Edwardsville, USA

    Albert C. J. Luo

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