| Description |
1 online resource |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Emerging methodologies and applications in modelling, identification and control ; volume 1 |
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Emerging methodologies and applications in modelling, identification and control.
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| Bibliography |
Includes bibliographical references and index. |
| Note |
Online resource; title from digital title page (viewed on December 07, 2021). |
| Summary |
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 comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications. Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems. |
| 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. |
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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. |
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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. |
| Subject |
Intelligent control systems -- Mathematics.
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Fractional calculus.
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Mathematical optimization.
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Commande intelligente -- Mathématiques.
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Dérivées fractionnaires.
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Optimisation mathématique.
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Fractional calculus
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Mathematical optimization
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| Added Author |
Radwan, Ahmed G., editor.
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Khanday, Farooq Ahmad, editor.
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Said, Lobna A., editor.
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| Other Form: |
Print version: 0128242930 9780128242933 (OCoLC)1241442744 |
| ISBN |
0128243341 (electronic book) |
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9780128242933 (electronic bk.) |
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0128242930 (electronic bk.) |
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9780128243343 (electronic bk.) |
| Standard No. |
AU@ 000070309860 |
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UKMGB 020388636 |
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