Advances in fractional calculus

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