Book 2007

Advances in Fractional Calculus

Theoretical Developments and Applications in Physics and Engineering

ISBN: 978-1-4020-6041-0 (Print) 978-1-4020-6042-7 (Online)

Table of contents (37 chapters)

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  1. Front Matter

    Pages i-xiii

  2. Analytical and Numerical Techniques

    1. Front Matter

      Pages 1-1

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      Chapter

      Pages 3-14

      Three Classes of FDEs Amenable to Approximation Using a Galerkin Technique

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      Chapter

      Pages 15-26

      Enumeration of the Real Zeros of the Mittag-Leffler Function Eα(z), 1 <α< 2

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      Chapter

      Pages 27-42

      The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equation

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      Chapter

      Pages 43-60

      Comparison of Five Numerical Schemes for Fractional Differential Equations

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      Chapter

      Pages 61-75

      Suboptimum H2 Pseudo-rational Approximations to Fractional-order Linear Time Invariant Systems

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      Chapter

      Pages 77-91

      Linear Differential Equations of Fractional Order

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      Chapter

      Pages 93-112

      Riesz Potentials as Centred Derivatives

  3. Classical Mechanics and Particle Physics

    1. Front Matter

      Pages 113-113

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      Chapter

      Pages 115-126

      On Fractional Variational Principles

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      Chapter

      Pages 127-138

      Fractional Kinetics in Pseudochaotic Systems and Its Applications

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      Chapter

      Pages 139-154

      Semi-integrals and Semi-derivatives in Particle Physics

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      Chapter

      Pages 155-167

      Mesoscopic Fractional Kinetic Equations versus a Riemann–Liouville Integral Type

  4. Diffusive Systems

    1. Front Matter

      Pages 169-169

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      Chapter

      Pages 171-184

      Enhanced Tracer Diffusion in Porous Media with an Impermeable Boundary

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      Chapter

      Pages 185-197

      Solute Spreading in Heterogeneous Aggregated Porous Media

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      Chapter

      Pages 199-212

      Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media

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      Chapter

      Pages 213-225

      Modelling and Identification of Diffusive Systems using Fractional Models

  5. Modeling

    1. Front Matter

      Pages 227-227

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      Chapter

      Pages 229-242

      Identification of Fractional Models from Frequency Data

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      Chapter

      Pages 243-256

      Dynamic Response of the Fractional Relaxor–Oscillator to a Harmonic Driving Force

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      Chapter

      Pages 257-270

      A Direct Approximation of Fractional Cole–Cole Systems by Ordinary First-order Processes

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      Chapter

      Pages 271-285

      Fractional Multimodels of the Gastrocnemius Muscle for Tetanus Pattern

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      Chapter

      Pages 287-302

      Limited-Bandwidth Fractional Differentiator: Synthesis and Application in Vibration Isolation

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