| Description |
1 online resource : illustrations |
| Series |
Emerging methodologies and applications in modelling, identification and control ; volume 2 |
| Contents |
Front Cover -- Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control -- Copyright -- Contents -- List of contributors -- 1 Continuous and discrete symmetry methods for fractional differential equations -- 1.1 Introduction -- 1.2 Continuous and discrete symmetry for classical differential equations -- 1.2.1 Continuous symmetry method -- 1.2.2 Discrete symmetry method -- 1.3 Continuous symmetry for fractional differential equation -- 1.3.1 Some basic results on fractional calculus -- 1.3.2 Continuous symmetry for fractional ordinary differential equations -- 1.3.3 Continuous symmetry for fractional partial differential equations -- 1.3.4 Some illustrative examples -- 1.4 Discrete symmetry for fractional Harry Dym equation -- 1.5 Conclusion -- References -- 2 Some theoretical and computation results about COVID-19 by using a fractional-order mathematical model -- 2.1 Introduction -- 2.2 Background materials -- 2.3 Main work -- 2.3.1 Qualitative analysis of (2.2) -- 2.3.2 Qualitative analysis for (2.3) -- 2.4 Series solution of the considered system (2.2) under normal Caputo derivative -- 2.4.1 Approximate solution and discussion for (2.2) -- Case I -- Case II -- Case III -- Case IV -- Case V -- 2.5 General series solution of the considered system (2.3) -- 2.5.1 Numerical results and discussion for (2.3) -- 2.5.2 Conclusion -- Declaration of competing interest -- References -- 3 Spatial-fractional derivatives for fluid flow and transport phenomena -- 3.1 Introduction -- 3.2 Preliminary concepts -- 3.3 Spatial-fractional mass conservation equation -- 3.4 Fractional Navier-Stokes equation -- 3.5 Special cases -- 3.5.1 Poiseuille flow -- 3.5.2 Boundary layer flow -- 3.6 Fractional models of flow in porous media -- 3.6.1 Fractional Darcy's law with time memory |
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3.6.2 Fractional Darcy law with space memory -- 3.7 Fractional natural gas equation -- 3.8 Fractional multiphase flows in porous media -- 3.9 Special cases of two-phase flow -- 3.9.1 Imbibition flow -- 3.9.2 Fractional momentum with time memory -- 3.9.3 Fractional mass equation with time memory -- 3.9.4 Fractional mass and momentum with time memory -- 3.9.5 Fractional mass and momentum with space memory -- 3.10 Fractional convection-diffusion equation -- 3.10.1 Fractional heat conduction model -- 3.10.2 Fractional transport equation -- 3.10.3 Applications in cooling and heating systems -- 3.11 Conclusion -- References -- 4 On the hybrid fractional chaotic systems: a numerical approach -- 4.1 Introduction -- 4.2 Preliminaries and notations -- 4.3 Hybrid fractional chaotic models -- 4.3.1 A hybrid fractional hyperchaotic finance system -- 4.3.2 Existence and uniqueness of the solution -- 4.3.3 Equilibrium points and stability -- 4.3.4 A hybrid fractional Bloch model with time delay -- 4.3.5 Existence and uniqueness of the time-delayed fractional solution -- 4.4 Numerical methods for solving hybrid fractional models -- 4.4.1 CPC-NSFDM -- 4.4.2 Stability of CPC-NSFDM -- 4.5 Numerical simulations -- 4.6 Conclusions -- Declaration of competing interest -- References -- 5 Iterative processes with fractional derivatives -- 5.1 Introduction -- 5.2 Preliminary concepts -- 5.3 Design and analysis of iterative methods using fractional derivatives -- 5.4 Numerical analysis of the proposed methods -- 5.4.1 Dependence on initial estimations -- 5.5 Concluding remarks -- Acknowledgments -- References -- 6 Design of fractional-order finite-time sliding mode controllers for quadrotor UAVs subjected to disturbances and uncertainties -- 6.1 Introduction -- 6.1.1 Motivation and background -- 6.1.2 Literature review -- 6.1.3 Contributions -- 6.1.4 Chapter organization |
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6.2 Preliminary results -- 6.3 Quadrotor system dynamics -- 6.4 Fractional-order SMC controllers for quadrotors -- 6.4.1 FOSMC-FOFTSMC design mechanism -- 6.4.1.1 Translational subsystem controller using FOSMC-FOFTSMC -- 6.4.1.2 Rotational subsystem controller using FOSMC-FOFTSMC -- 6.4.2 IFOSMC design structure for UAV systems -- 6.4.2.1 IFOSMC control for translational systems -- 6.4.2.2 IFOSMC structure for attitude subsystem -- 6.5 Simulation results and discussion -- 6.5.1 Simulation 1 -- 6.5.2 Simulation 2 -- 6.6 Conclusion -- References -- 7 Performance evaluation of fractional character vector control applied for doubly fed induction generator operating in a network-connected wind power system -- 7.1 Introduction -- 7.2 Variable-speed wind power system modeling -- 7.2.1 Wind turbine modeling -- 7.2.2 Dynamic modeling of DFIGs -- 7.2.3 Maximum power point tracking law -- 7.3 Vector control scheme of DFIG using fractional-order PI controllers -- 7.3.1 A brief about fractional calculus -- 7.3.2 Concept of vector control of DFIG -- 7.4 Design of FOPI controllers applied in the power and current regulation loops -- 7.4.1 Design of a fractional-order PI controller as current regulator -- 7.4.2 Design of a fractional-order PI controller as power regulator -- 7.5 Numerical results and analysis -- 7.5.1 Robustness evaluation against generator parameter variations -- 7.5.2 Robustness evaluation against network voltage drop -- 7.5.3 Comparative studies -- 7.6 Conclusion -- References -- 8 Finite time synchronization of discontinuous fractional order Cohen-Grossberg memristive neural networks with discrete delays under sliding mode control strategies -- 8.1 Introduction -- 8.1.1 Related works -- 8.2 Preliminaries -- 8.2.1 Basic tools for fractional-order derivatives -- 8.2.2 Mittag-Leffler function -- 8.2.3 Model formulation -- 8.3 Main results |
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8.3.1 Existence of Filippov solutions -- 8.3.2 Finite time stability criteria for the sliding motion -- 8.3.3 Reachability criteria -- 8.4 A numerical example -- 8.5 Conclusions -- Acknowledgments -- References -- 9 Variable-order control systems: a steady-state error analysis -- 9.1 Introduction -- 9.2 Variable-order operators -- 9.3 Main results -- 9.4 A method for numerical simulation -- 9.5 Numerical examples -- 9.6 Conclusion -- References -- 10 Theoretical study in conformal thermal antennas optimized by a fractional energy -- 10.1 Introduction -- 10.2 Conformal mapping -- 10.3 Thermal optimization approach -- 10.4 CTA optimization -- 10.4.1 Cylindrical CTA -- 10.4.2 Quasicylindrical CTA -- 10.5 Conformal fractional energy -- 10.6 Conclusion -- References -- 11 Optimal design of fractional-order Butterworth filter with improved accuracy and stability margin -- 11.1 Introduction -- 11.2 Proposed technique -- 11.2.1 Determination of optimal coefficients using FPA -- 11.2.2 Polynomial fitting -- 11.3 Simulation results and discussion -- 11.3.1 Design accuracy -- 11.3.2 Stability margin -- 11.3.3 Cut-off frequency -- 11.3.4 Circuit realization -- 11.4 Conclusions -- References -- 12 Pseudospectral methods for the Riesz space-fractional Schrödinger equation -- 12.1 Introduction -- 12.2 Space-fractional couplers -- 12.3 Gegenbauer polynomials and their properties -- 12.4 Numerical schemes -- 12.4.1 Spatial discretization -- 12.4.1.1 Nonlinear fractional Riesz space Schrödinger equations -- 12.4.1.2 Coupled nonlinear fractional Riesz space Schrödinger equations -- 12.4.2 Temporal discretization -- 12.5 Numerical experiments -- 12.5.1 Convergence test -- 12.5.2 A single equation -- 12.5.3 Coupled equations -- 12.6 Conclusion and discussion -- References |
| Notes |
1. Fractional-order calculus, numerical techniques, and applications 2. Fractional-order linear circuits and systems: Design and hardware implementation 3. Fractional-order chaotic systems and their applications 4. Bio-impedance Modeling 5. Fractional order modeling of different systems 6. Fractional order Chaos control and synchronization 7. Fractional order image processing and implementations 8. Applications based on fractional-order memristive systems 9. Solid-state implementations of fractional-order elements 10. Fractional-order non-linear circuits and systems: design and hardware implementation 11. Fractional-order systems and applications based on neural networks 12. Fractional-order controllers, theory, design, and applications 13. Platforms for fractional-order system design 14. Fractional-order modeling of supercapacitors and batteries |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based on online resource; title from digital title page (viewed on May 05, 2022) |
| Subject |
Intelligent control systems -- Mathematical models
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Fractional calculus.
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Fractional calculus
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| Form |
Electronic book
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| 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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| ISBN |
9780323902038 |
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0323902030 |
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