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.
Зміст
Analytical and Numerical Techniques.- Three Classes of FDEs Amenable to Approximation Using a Galerkin Technique.- Enumeration of the Real Zeros of the Mittag-Leffler Function E?(z), 1Operators on Field Programmable Gate Arrays.- Complex Order-Distributions Using Conjugated order Differintegrals.- Viscoelastic and Disordered Media.- Fractional Derivative Consideration on Nonlinear Viscoelastic Statical and Dynamical Behavior under Large Pre-Displacement.- Quasi-Fractals: New Possibilities in Description of Disordered Media.- Fractional Damping: Stochastic Origin and Finite Approximations.- Analytical Modelling and Experimental Identification of Viscoelastic Mechanical Systems.- Control.- LMI Characterization of Fractional Systems Stability.- Active Wave Control for Flexible Structures Using Fractional Calculus.- Fractional-order Control of a Flexible Manipulator.- Tuning Rules for Fractional PIDs.- Frequency Band-Limited Fractional Differentiator Prefilter in Path Tracking Design.- Flatness Control of a Fractional Thermal System.- Robustness Comparison of Smith Predictor-based Control and Fractional-Order Control.- Robust Design of an Anti-windup Compensated 3rd-Generation Crone Controller.- Robustness of Fractional-order Boundary Control of Time Fractional Wave Equations with Delayed Boundary Measurement Using the Simple Predictor.
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