Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering

✍ Scribed by Satwinder Jit Singh, Anindya Chatterjee (auth.), Jocelyn Sabatier, Om Prakash Agrawal, J. A. Tenreiro Machado (eds.)

• Publisher: Springer Netherlands
• Year: 2007
• Tongue: English
• Leaves: 549
• Edition: 1
• Category: Library

✦ Synopsis

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation.

As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

✦ Table of Contents

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Three Classes of FDEs Amenable to Approximation Using a Galerkin Technique....Pages 3-14
Enumeration of the Real Zeros of the Mittag-Leffler Function Eα(z), 1 <α< 2....Pages 15-26
The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equation....Pages 27-42
Comparison of Five Numerical Schemes for Fractional Differential Equations....Pages 43-60
Suboptimum H2 Pseudo-rational Approximations to Fractional-order Linear Time Invariant Systems....Pages 61-75
Linear Differential Equations of Fractional Order....Pages 77-91
Riesz Potentials as Centred Derivatives....Pages 93-112
Front Matter....Pages 113-113
On Fractional Variational Principles....Pages 115-126
Fractional Kinetics in Pseudochaotic Systems and Its Applications....Pages 127-138
Semi-integrals and Semi-derivatives in Particle Physics....Pages 139-154
Mesoscopic Fractional Kinetic Equations versus a Riemann–Liouville Integral Type....Pages 155-167
Front Matter....Pages 169-169
Enhanced Tracer Diffusion in Porous Media with an Impermeable Boundary....Pages 171-184
Solute Spreading in Heterogeneous Aggregated Porous Media....Pages 185-197
Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media....Pages 199-212
Modelling and Identification of Diffusive Systems using Fractional Models....Pages 213-225
Front Matter....Pages 227-227
Identification of Fractional Models from Frequency Data....Pages 229-242
Dynamic Response of the Fractional Relaxor–Oscillator to a Harmonic Driving Force....Pages 243-256
A Direct Approximation of Fractional Cole–Cole Systems by Ordinary First-order Processes....Pages 257-270
Fractional Multimodels of the Gastrocnemius Muscle for Tetanus Pattern....Pages 271-285
Limited-Bandwidth Fractional Differentiator: Synthesis and Application in Vibration Isolation....Pages 287-302
Front Matter....Pages 303-303
A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits....Pages 305-322
Electrical Skin Phenomena: A Fractional Calculus Analysis....Pages 323-332
Implementation of Fractional-order Operators on Field Programmable Gate Arrays....Pages 333-346
Complex Order-Distributions Using Conjugated order Differintegrals....Pages 347-360
Front Matter....Pages 361-361
Fractional Derivative Consideration on Nonlinear Viscoelastic Statical and Dynamical Behavior under Large Pre-Displacement....Pages 363-376
Quasi-Fractals: New Possibilities in Description of Disordered Media....Pages 377-388
Fractional Damping: Stochastic Origin and Finite Approximations....Pages 389-402
Analytical Modelling and Experimental Identification of Viscoelastic Mechanical Systems....Pages 403-416
Front Matter....Pages 417-417
LMI Characterization of Fractional Systems Stability....Pages 419-434
Active Wave Control for Flexible Structures Using Fractional Calculus....Pages 435-448
Fractional-order Control of a Flexible Manipulator....Pages 449-462
Tuning Rules for Fractional PIDs....Pages 463-476
Frequency Band-Limited Fractional Differentiator Prefilter in Path Tracking Design....Pages 477-492
Flatness Control of a Fractional Thermal System....Pages 493-509
Robustness Comparison of Smith Predictor-based Control and Fractional-Order Control....Pages 511-526
Robust Design of an Anti-windup Compensated 3rd-Generation Crone Controller....Pages 527-542
Robustness of Fractional-order Boundary Control of Time Fractional Wave Equations with Delayed Boundary Measurement Using the Simple Predictor....Pages 543-552

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering;Simulation and Modeling;Systems Theory, Control;Theoretical, Mathematical and Computational Physics;Mechanical Engineering;Electrical Engineering