Fractional order systems : an overview of mathematics, design, and applications for engineers /
Fractional Order Systems: An Overview of Mathematics, Design, and Applications for Engineers introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices compr...
Call Number: | Libro Electrónico |
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Other Authors: | , , |
Format: | Electronic eBook |
Language: | Inglés |
Published: |
London ; San Diego, CA :
Academic Press,
[2022]
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Series: | Emerging methodologies and applications in modelling, identification and control.
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Subjects: | |
Online Access: | Texto completo |
Table of Contents:
- Front Cover
- Fractional Order Systems
- Copyright
- Contents
- List of contributors
- 1 A survey on numerical studies for fractional biological models and their optimal control
- 1.1 Introduction
- 1.2 Primary definitions of fractional calculus
- 1.3 Fractional optimal control problem
- 1.4 A survey on fractional biological models and their optimal control
- 1.5 A survey on numerical methods for solving fractional optimal control biological models
- 1.5.1 Iterative optimal control method
- 1.5.2 Nonstandard finite difference method
- 1.5.2.1 Grunwald-Letnikov nonstandard finite difference method
- 1.5.3 Nonstandard weighted average finite difference method
- 1.5.4 Nonstandard implicit compact finite difference method
- 1.5.5 Nonstandard generalized Euler method
- 1.5.6 Two-step nonstandard Lagrange interpolation method
- 1.5.7 Shifted Jacobi collocation method
- 1.5.7.1 Jacobi spectral method with fractional derivative
- 1.6 A novel fractional-order malaria mathematical model
- 1.7 HFOCP
- 1.7.1 Numerical methods for solving HFOCP
- 1.7.2 CPC-NSFDM
- 1.7.3 C-NSFDM
- 1.7.4 Stability analysis for CPC-NSFDM
- 1.8 Numerical experiment and discussion
- 1.9 Conclusions
- References
- 2 A collection of interdisciplinary applications of fractional-order circuits
- 2.1 Introduction
- 2.2 Implementation of the approximated Laplacian operator
- 2.3 Biomedical signal processing applications
- 2.3.1 Mihalas-Niebur neuron model
- 2.3.2 Extraction of R peaks in ECG signals
- 2.3.3 Phantom EEG system model
- 2.4 Bio-impedance applications
- 2.4.1 Artificial human eardrum model
- 2.4.2 Biceps tissue model
- 2.4.3 Cardiac tissue electrode interface model
- 2.4.4 Lung model of the human respiratory tree
- 2.5 Sensor applications
- 2.6 Conclusions and discussion
- Acknowledgments
- References
- 3 Fractional-order control.
- 3.1 Introduction
- 3.2 Fractional-order systems and controllers
- 3.2.1 Fractional calculus
- 3.2.2 Fractional-order systems
- 3.2.3 Fractional-order controllers
- 3.2.4 Numerical solution of fractional-order differential equations
- 3.3 New fractional-order control techniques
- 3.3.1 Nonlinear fractional-order controller
- Definition
- Illustrative example
- 3.3.2 Fractional-order adaptive control
- Definition
- Illustrative example
- 3.3.3 Fractional-order extremal control
- Definition
- Illustrative example
- 3.4 Discussion and conclusions
- Acknowledgment
- References
- 4 Fractional-order systems, numerical techniques, and applications
- 4.1 Introduction
- 4.2 Numerical methods for solving the multiterm time-fractional diffusion-wave equation
- 4.2.1 A two-term mobile/immobile time-fractional advection-dispersion equation
- 4.2.2 A two-term time-fractional diffusion-wave equation
- 4.2.3 Multiterm time-fractional diffusion-wave equation
- 4.2.4 Numerical examples
- 4.3 Analytical solution of the multiterm time-fractional differential equation and application to unsteady flow of generalized viscoelastic fluid
- 4.3.1 Multiterm time-fractional dynamic models
- 4.3.2 Separation of variables method
- 4.3.3 Analytical solution of the multiterm time-fractional equation
- 4.3.3.1 Definitions and theorem
- 4.3.3.2 Solutions of fractional models
- 4.3.4 Numerical examples
- 4.4 Numerical analysis of multiterm time-fractional viscoelastic non-Newtonian fluid models for simulating unsteady MHD Couette flow of generalized Oldroyd-B fluid
- 4.4.1 Preliminaries
- 4.4.2 Derivation of the numerical schemes
- 4.4.2.1 Scheme I: First-order implicit scheme
- 4.4.2.2 Scheme II: Mixed L scheme
- 4.4.3 Theoretical analysis
- 4.4.3.1 Solvability
- 4.4.3.2 Stability
- 4.4.3.3 Convergence
- 4.4.4 Numerical examples.
- 4.5 A fractional alternating-direction implicit method for a multiterm time-space fractional Bloch-Torrey equation in 3D
- 4.5.1 Fractional alternating-direction implicit method
- 4.5.2 Stability and convergence of the fractional alternating-direction implicit method
- 4.5.3 Numerical examples
- References
- 5 Fractional-order systems, numerical techniques, and applications
- 5.1 Introduction
- 5.2 Unstructured-mesh Galerkin finite element method for the 2D multiterm time-space fractional Bloch-Torrey equations on irregular convex domains
- 5.2.1 Preliminaries
- 5.2.2 Finite element method
- 5.2.2.1 The fully discrete finite element scheme
- 5.2.2.2 The FEM with an unstructured mesh
- 5.2.3 Stability and convergence
- 5.2.4 The FEM for a 2D coupled system of multiterm time-space fractional Bloch-Torrey equations
- 5.2.5 Numerical examples
- 5.3 Finite difference/finite element method for a 2D multiterm time-fractional mixed subdiffusion and diffusion-wave equation on convex domains
- 5.3.1 Preliminaries
- 5.3.2 The finite element method
- 5.3.2.1 Finite element Scheme I
- 5.3.2.2 Implementation of the finite element scheme
- 5.3.2.3 Finite element Scheme II
- 5.3.3 Stability and convergence
- 5.3.4 Numerical examples
- 5.4 Alternating-direction implicit spectral Galerkin method for the multiterm time-space fractional diffusion equation in three dimensions
- 5.4.1 Preliminaries
- 5.4.2 Numerical scheme
- 5.4.2.1 Variational formulation
- 5.4.2.2 Time semidiscrete scheme
- 5.4.2.3 Fully discrete scheme
- 5.4.2.4 Theoretical results
- 5.4.3 Implementation
- 5.4.3.1 Computing the mass and stiff matrices
- 5.4.3.2 Implementation of the ADI method
- 5.4.4 Numerical examples
- 5.5 Space-time spectral method for the multiterm time-fractional diffusion equations
- 5.5.1 Preliminaries.