| Description |
1 online resource (365 pages) |
| Contents |
880-01 Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; Acknowledgments; About the Authors; 1. Mathematical Postulations; 1.1 Special Functions; 1.1.1 Gamma Function; 1.1.2 Beta Function; 1.1.3 Mittag-Leffler Function; 1.1.4 Hypergeometric Function; 1.1.5 Error Function and Complementary Error Function; 1.1.6 Bessel Functions; 1.2 Definitions and Properties of Fractional-Order Operators; 1.2.1 Grunwald-Letnikov (GL) Fractional-Order Derivative; 1.2.2 Riemann-Liouville (RL) Fractional-Order Integral; 1.2.3 Riemann-Liouville Fractional-Order Derivative |
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880-01/(S 1.2.4 Caputo Fractional-Order Derivative1.2.5 Properties of GL, RL, and Caputo Fractional-Order Derivatives; 1.3 Laplace Transforms of Fractional-Order Operators; 1.4 Fractional-Order Systems; 1.5 Fractional-Order PIλ, PDμ, and PIλDμ Controller; 1.6 Triangular Orthogonal Functions; 1.6.1 Review of Block Pulse Functions; 1.6.2 Complementary Pair of Triangular Orthogonal Function Sets; 1.6.3 Expansion of Two Variable Function via TFs; 1.6.4 The TF Estimate of the First-Order Integral of Function f(t); 1.6.5 The TF Estimate of Riemann-Liouville Fractional-Order Integral of f(t) |
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1.6.6 Error Analysis1.6.7 MATLAB® Code for Generalized Triangular Function Operational Matrices; 1.7 Triangular Strip Operational Matrices for Classical and Fractional Derivatives; 1.7.1 Operational Matrix for Classical Derivative; 1.7.2 Operational Matrix for Fractional-Order Derivative; 1.7.3 MATLAB Code for Triangular Strip Operational Matrices; References; 2. Numerical Method for Simulation of Physical Processes Represented by Weakly Singular Fredholm, Volterra, and Volterra-Fredholm Integral Equations; 2.1 Existence and Uniqueness of Solution; 2.2 The Proposed Numerical Method |
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2.3 Convergence Analysis2.4 Numerical Experiments; 2.4.1 Investigation of Validity and Accuracy; Example 2.1: The weakly singular (WS) Fredholm-Hammerstein integral equation (IE) of 2nd kind; Example 2.2: WS linear Fredholm IE of 2nd kind; Example 2.3: WS Fredholm-Hammerstein IE of 1st kind; Example 2.4: WS Volterra-Fredholm-Hammerstein IE of 2nd kind; Example 2.5: WS Volterra-Hammerstein IE of 2nd kind; 2.4.2 Numerical Stability Analysis; Example 2.6: WS linear Volterra-Fredholm IE of 2nd kind; 2.4.3 Application of Proposed Method to Physical Process Models |
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Application 2.1: Heat radiation in a semi-infinite solidApplication 2.2: Hydrodynamics; Application 2.3: Lighthill singular integralequation; 2.5 MATLAB® Codes for Numerical Experiments; 2.6 Summary of Deliverables; References; 3. Numerical Method for Simulation of Physical Processes Modeled by Abel's Integral Equations; 3.1 Existence and Uniqueness of Solution; 3.2 The Proposed Numerical Method; 3.3 Convergence Analysis; 3.4 Numerical Experiments; 3.4.1 Investigation of Validity and Accuracy; 3.4.2 Numerical Stability Analysis |
| Summary |
The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems. Key features Proposes generalized triangular function operational matrices. Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes. Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel's integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations. Suggests alternative way to do numerical computation of fractional order signals and systems and control. Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results |
| Notes |
3.4.3 Application to Physical Process Models Involving Abel's Integral Equations |
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Print version record |
| Subject |
Fractional calculus.
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Intelligent control systems -- Mathematics
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Chaotic behavior in systems -- Mathematical models
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TECHNOLOGY & ENGINEERING -- Electrical.
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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Chaotic behavior in systems -- Mathematical models
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Fractional calculus
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| Form |
Electronic book
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| Author |
Kundu, Madhusree
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| ISBN |
9780429996894 |
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0429996896 |
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