Book description
This book introduces an original fractional calculus methodology (‘the infinite state approach’) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation.Table of contents
 Cover
 Foreword
 Preface

PART 1: Simulation and Identification of Fractional Differential Equations (FDEs) and Systems (FDSs)
 1 The Fractional Integrator

2 Frequency Approach to the Synthesis of the Fractional Integrator
 2.1. Introduction
 2.2. Frequency synthesis of the fractional derivator
 2.3. Frequency synthesis of the fractional integrator
 2.4. State space representation of
 2.5. Modal representation of
 2.6. Numerical algorithm
 2.7. Frequency validation
 2.8. Time validation
 2.9. Internal state variables
 A.2. Appendix: design of fractional integrator parameters
 3 Comparison of Two Simulation Techniques

4 Fractional Modeling of the Diffusive Interface
 4.1. Introduction
 4.2. Heat transfer and diffusive model of the plane wall
 4.3. Fractional commensurate order models
 4.4. Optimization of the fractional commensurate order model
 4.5. Fractional noncommensurate order models
 4.6. Conclusion
 A.4. Appendix: estimation of frequency responses – the leastsquares approach
 5 Modeling of Physical Systems with Fractional Models: an Illustrative Example

PART 2: The Infinite State Approach

6 The Distributed Model of the Fractional Integrator
 6.1. Introduction
 6.2. Origin of the frequency distributed model
 6.3. Frequency distributed model
 6.4. Finite dimension approximation of the fractional integrator
 6.5. Frequency synthesis and distributed model
 6.6. Numerical validation of the distributed model
 6.7. Riemann–Liouville integration and convolution
 6.8. Physical interpretation of the frequency distributed model
 A.6. Appendix: inverse Laplace transform of the fractional integrator

7 Modeling of FDEs and FDSs
 7.1. Introduction
 7.2. Closedloop modeling of an elementary FDS
 7.3. Closedloop modeling of an FDS
 7.4. Transients of the onederivative FDS
 7.5. Transients of a twoderivative FDS
 7.6. External or openloop modeling of commensurate fractional order FDSs
 7.7. External and internal representations of an FDS
 7.8. Computation of the MittagLeffler function
 A.7. Appendix: inverse Laplace transform of

8 Fractional Differentiation
 8.1. Introduction
 8.2. Implicit fractional differentiation
 8.3. Explicit Riemann–Liouville and Caputo fractional derivatives
 8.4. Initial conditions of fractional derivatives
 8.5. Initial conditions in the general case
 8.6. Unicity of FDS transients
 8.7. Numerical simulation of Caputo and Riemann–Liouville transients
 9 Analytical Expressions of FDS Transients

10 Infinite State and Fractional Differentiation of Functions
 10.1. Introduction
 10.2. Calculation of the Caputo derivative
 10.3. Initial conditions of the Caputo derivative
 10.4. Transients of fractional derivatives
 10.5. Calculation of fractional derivatives with the implicit derivative
 10.6. Numerical validation of Caputo derivative transients
 A.10. Appendix: convolution lemma

6 The Distributed Model of the Fractional Integrator
 References
 Index
 End User License Agreement
Product information
 Title: Analysis, Modeling and Stability of Fractional Order Differential Systems 1
 Author(s):
 Release date: September 2019
 Publisher(s): WileyISTE
 ISBN: 9781786302694
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