Advances in Fractional Calculus

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.

Preface; 1. Analytical and Numerical Techniques: Three Classes of FDEs Amenable to Approximation Using a Galerkin Technique, by S. I Singh, A. Chatterjee; Enumeration of the Real Zeros of the Mittag-Leffler Function, by J W. Hanneken, D. M Vaught, B. N. Narahari Achar; The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equations, by B. N. Narahari Achar, C. F. Lorenzo, T. T. Hartley; Comparison of Five Numerical Schemes for Fractional Differential Equations, by O. P. Agrawal, P. Kumar; Sub-Optimum H2 Pseudo-Rational Approximations to Fractional Order Linear Time Invariant Systems, by D. Xue, Y. Chen; Linear Differential Equations of Fractional Order, by B. Bonilla, M. Rivero, J.J. Trujillo; Riesz Potentials as Centred Derivatives, by M.D. Ortigueira; 2. Classical Mechanics and Particle Physics: On Fractional Variational Principles, by D. Baleanu, S. Muslih; Fractional Kinetics In Pseudochaotic Systems And Its Applications, by G. M Zaslavsky; Semi-Integrals and Semi-Derivatives in Particle Physics, by P. W. Krempl; Mesoscopic Fractional Kinetic Equations versus a Riemarin-Liouville Integral Type, by R. R. Nigmatullin, J.J. Trujillo; 3. Diffusive Systems: Enhanced Yracer Diffusion in Porous Media with an Impermeable Boundary, by N. Krepysheva, L. Di Pietro, M C. Néel; Solute Spreding in Heterogeneous Aggregated Porous Media, by K. Logvinova, M C. Néel; Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media, by F. San Jose Martinez, 1’. Pachepsky, W. Rawls Modelling and Identification of Diffusive Systems using Fractional Models, by A. Benchellal, T. Poinot, .1 C. Trigeassou; 4 . Modeling: Identification of Fractional Models from Frequency Data, by D. Valério, I Sá da Costa; Dynamic Response of the Fractional Relaxor-Oscillator to a Harmonic Driving Force, by B. N. Narahari Achar, J.W. Hanneken; A Direct Approximation of Fractional Cole-Cole-Systems byOrdinary First Order Processes, by M Haschka, V. Krebs; Fractional Multi-Models of the Gastrocnemius Muscle for Tetanus Pattern, by L. Sommacal, P. Meichior, I M Cabelguen, A. Oustaloup, A. IJspeert; Limited-Bandwidth Fractional Differentiator: Synthesis and Application in Vibration Isolation, by P. Serrier, X Moreau, A. Oustaloup; 5. Electrical Systems: A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits, by C. Reis, J A. Tenreiro Machado, I B. Cunha; Electrical Skin Phenomena: A Fractional Calculus Analysis, by J. A. Tenreiro Machado, I S. Jesus, A. Gaihano, I B. Cunha, I K Tar; Implementation of Fractional-Order Operators on Field Programmable GateArrays, by C. X Jiang, J E. Carletta, T. T. Hartley, Complex Order-Distributions Using Conjugated-Order Differintegrals, by I L. Adams, i: i: Hartley, C. F. Lorenzo; 6. Viscoelastic and Disordered Media: Fractional Derivative Consideration on Nonlinear Viscoelastic Statical and Dynamical Behavior under Large Pre-displacement, by H. Nasuno, N. Shimizu, M Fukunaga; Quasi-Fractals: New Possibilities in Description of Disordered Media, by R. R. Nigmatullin, A. P. Ale/chin Fractional Damping: Stochastic Origin, and Finite Approximations, by S. J. Singh, A. Chatterjee; Analytical Modeling and Experimental Identification of Viscoelastic Mechanical Systems, by G. Catania, S. Sorrentino; 7. Control: LMI Characterization ofFractional Systems Stability, by M Moze, J. Sabatier, A. Oustaloup; Active Wave Control for Flexible Structures Using Fractional Calculus, by M Kuroda; Fractional Order Control of a Flexible Manipulator, by V. Feliu, B.M. Vinagre, C.A. Monje; Tuning-Rules for Fractional PIDs, by D. Valério, I Sá da Costa; Frequency Band-Limited Fractional Differentiator Prefilter in Path Tracking Design, by P. Melchior, A. Poty, A. Oustaloup; Flatness Control of a Fractional Thermal System, by P. Melchior, M Cugnet, I. Sabatier, A. Poty, A. Oustaloup; Robustness