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Theory and Applications of Non-integer Order Systems

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Cover of '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
Attention for Chapter 15: Linear and Nonlinear Fractional Voigt Models
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Chapter title
Linear and Nonlinear Fractional Voigt Models
Chapter number 15
Book title
Theory and Applications of Non-integer Order Systems
Published in
arXiv, January 2017
DOI 10.1007/978-3-319-45474-0_15
Book ISBNs
978-3-31-945473-3, 978-3-31-945474-0
Authors

Amar Chidouh, Assia Guezane-Lakoud, Rachid Bebbouchi, Amor Bouaricha, Delfim F. M. Torres

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X Demographics

The data shown below were collected from the profiles of 2 X users who shared this research output. Click here to find out more about how the information was compiled.
 Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 5 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 5 100%

Demographic breakdown

Readers by professional status Count As %
Professor 1 20%
Researcher 1 20%
Student > Postgraduate 1 20%
Unknown 2 40%
Readers by discipline Count As %
Mathematics 3 60%
Computer Science 1 20%
Unknown 1 20%
Attention Score in Context

Attention Score in Context

This research output has an Altmetric Attention Score of 1. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 21 June 2016.
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#18,464,797
of 22,879,161 outputs
Outputs from arXiv
#535,667
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#310,498
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Outputs of similar age from arXiv
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So far Altmetric has tracked 939,641 research outputs from this source. They receive a mean Attention Score of 3.9. This one is in the 28th percentile – i.e., 28% of its peers scored the same or lower than it.
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