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...

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Bibliographic Details
Call Number:Libro Electrónico
Other Authors: Radwan, Ahmed G. (Editor), Khanday, Farooq Ahmad (Editor), Said, Lobna A. (Editor)
Format: Electronic eBook
Language:Inglés
Published: London ; San Diego, CA : Academic Press, [2022]
Series:Emerging methodologies and applications in modelling, identification and control.
Subjects:
Intelligent control systems > Mathematics.
Fractional calculus.
Mathematical optimization.
Commande intelligente > Math�ematiques.
D�eriv�ees fractionnaires.
Optimisation math�ematique.
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.

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