Theory and Applications of Non-integer Order Systems

Table of Contents

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   Book Overview
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   Chapter 1 Existence of Solutions of Abstract Fractional Impulsive Integrodifferential Equations of Sobolev Type
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   Chapter 2 Quadrature Based Approximations of Non-integer Order Integrator on Finite Integration Interval
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   Chapter 3 On the Fractional Continuous-Time Hegselmann–Krause’s Type Consensus Model
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   Chapter 4 Harmonic Numbers of Any Order and the Wolstenholme’s-Type Relations for Harmonic Numbers
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   Chapter 5 Cayley–Hamilton Theorem for Fractional Linear Systems
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   Chapter 6 Order Composition Properties for Output-Additive Variable-Order Derivative
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   Chapter 7 Variable-, Fractional-Order Oscillation Element
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   Chapter 8 Variable-, Fractional-Order Inertial Element
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    Chapter 9 Remarks on Mittag-Leffler Discrete Function and Putzer Algorithm for Fractional h-Difference Linear Equations
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    Chapter 10 On the Output-Additive Switching Strategy for a New Variable Type and Order Difference
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    Chapter 11 Large Deviations for Stochastic Fractional Differential Equations
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    Chapter 12 Mean Square Stability of Discrete-Time Fractional Order Systems With Multiplicative Noise
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    Chapter 13 Conformable Fractional Wave-Like Equation on a Radial Symmetric Plate
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    Chapter 14 Reconstruction Robin Boundary Condition in the Heat Conduction Inverse Problem of Fractional Order
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    Chapter 15 Linear and Nonlinear Fractional Voigt Models
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    Chapter 16 Digital Fractional Integrator
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    Chapter 17 Optimal Control for Discrete Fractional Systems
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    Chapter 18 Fractional Order Back Stepping Sliding Mode Control for Blood Glucose Regulation in Type I Diabetes Patients
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    Chapter 19 Maximum and Minimum Principles for the Generalized Fractional Diffusion Problem with a Scale Function-Dependent Derivative
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    Chapter 20 On a New Class of Multistage Fractional-Order Phase-Lead Compensators
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    Chapter 21 On the Existence of Optimal Controls for the Fractional Continuous-Time Cucker–Smale Model
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    Chapter 22 Determining the Time Elapsed Since Sudden Localized Impulse Given to Fractional Advection Diffusion Equation
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    Chapter 23 Accuracy Analysis for Fractional Order Transfer Function Models with Delay
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    Chapter 24 Accuracy Estimation of Digital Fractional Order PID Controller
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    Chapter 25 Modeling of Fractional-Order Integrators and Differentiators Using Tustin-Based Approximations and Model Order Reduction Techniques
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    Chapter 26 Tempered Fractional Model of Transient Current in Organic Semiconductor Layers
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    Chapter 27 Modeling Heat Transfer Process in Grid-Holes Structure Changed in Time Using Fractional Variable Order Calculus
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    Chapter 28 Analysis of Performance Indicators for Tuning Non-integer Order Controllers
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    Chapter 29 Controllability of Nonlinear Fractional Delay Dynamical Systems with Multiple Delays in Control
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    Chapter 30 New Controllability Criteria for Fractional Systems with Varying Delays
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    Chapter 31 Controllability of Nonlinear Stochastic Fractional Integrodifferential Systems in Hilbert Spaces
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    Chapter 32 Finding a Set of (A, B, C, D) Realisations for Fractional One-Dimensional Systems with Digraph-Based Algorithm
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    Chapter 33 Relative Controllability of Nonlinear Fractional Delay Dynamical Systems with Time Varying Delay in Control
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    Chapter 34 Stability Analysis for the New Model of Fractional Discrete-Time Linear State-Space Systems
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    Chapter 35 Fractional Differential-Algebraic Systems with Delay: Computation of Final Dimension Initial Conditions and Inputs for Given Outputs
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    Chapter 36 Robot Path Control with Al-Alaoui Rule for Fractional Calculus Discretization
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    Chapter 37 Implementation of Bi-fractional Filtering on the Arduino Uno Hardware Platform
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    Chapter 38 Fractional Prabhakar Derivative and Applications in Anomalous Dielectrics: A Numerical Approach
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    Chapter 39 Finite Element Method for Time Fractional Keller–Segel Chemotaxis System
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    Chapter 40 Adaptive Fractional Order Sliding Mode Controller Design for Blood Glucose Regulation-4-3
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    Chapter 41 Expansion of Digraph Size of 1-D Fractional System with Delay
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    Chapter 42 A Discrete-Time Fractional Order PI Controller for a Three Phase Synchronous Motor Using an Optimal Loop Shaping Approach
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    Chapter 43 Application of SubIval, a Method for Fractional-Order Derivative Computations in IVPs
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    Chapter 44 Application of the Time-Fractional Diffusion Equation to Methyl Alcohol Mass Transfer in Silica