Cargando…
Fractional calculus theory /
The first volume of this two-volume book, presents history, the mathematical modeling and the applications of fractional order systems, and contains mathematical and theoretical studies and research related to this domain. This volume is made up of 11 chapters. The first chapter presents an analysis...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Nova Publishers,
[2015]
|
| Colección: | Mathematics research developments series.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- FRACTIONAL CALCULUS: THEORY; FRACTIONAL CALCULUS: THEORY; LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA; CONTENTS; FOREWORD; PREFACE; ABOUT THE EDITORS; Chapter 1: ANALYSIS OF THE CAPUTO DERIVATIVE AND PSEUDO STATE REPRESENTATION WITH THE INFINITE STATE APPROACH; Abstract; Introduction; Riemann-Liouville Integral and Infinite State Approach; Laplace Transform of the Caputo Derivative; Initial Conditions for FDE/FDS Simulation; The Transition Matrix of a Commensurate Order System; Conclusion; References; Chapter 2: STABILITY OF A CLASS OF FRACTIONAL CAUCHY PROBLEM; Abstract; Methods.
- Existence of SolutionsUlam-Hyers Stability; Conclusion; References; Chapter 3: NUMERICAL SOLUTION OF FRACTIONAL ORDER DIFFERENTIAL EQUATIONS VIA MATRIX-BASED METHODS; Abstract; 1. Introduction; 2. Fractional Integration and DifferentiationMatrices; 3. Discretization and Solution of FDE; 4. Numerical Examples; 5. Conclusion; Acknowledgments; References; Chapter 4: ON ANALYTICAL METHODS FOR DIFFERENTIAL EQUATIONS WITH LOCAL FRACTIONAL DERIVATIVE OPERATORS; Abstract; Introduction; Local Fractional Derivatives and Integrals; Local Fractional Integral Transforms; Applications; Conclusion.
- 2. Basic Properties of Fractional Difference Operators3. Linear Fractional Difference Equations; 4. Stability of Single-TermFractional Difference Equations; 5. Stability of Multi-Term Fractional Difference Equations; 6. Conclusion; Acknowledgment; References; Chapter 7: USING THE HANKEL OPERATOR TO INITIALIZE FRACTIONAL-ORDER SYSTEMS; Abstract; 1. Introduction; 2. Impulse Response Approximation; 3. Output-Based Initialization; 4. Output-Based Initialization Examples; 5. Conclusion; References.
- Chapter 8: FRACTIONAL REACTION-TRANSPORT EQUATIONS ARISING FROM EVANESCENT CONTINUOUS TIME RANDOM WALKSAbstract; 1. Introduction; 2. Integral Equation for a CTRW with Evanescence; 3. Fractional Diffusion Equations with Evanescence; 4. Applications; 5. Summary and Outlook; References; Chapter 9: EXPONENTIAL INTEGRATORS FOR FRACTIONAL DIFFERENTIAL EQUATIONS; Abstract; Differential equations; 2. Linear Systems of FDEs: Theoretical Aspects; 3. Exponential Integrators: A Short ReviewThe history; 4. Exponential Product Integration for FDEs; 5. Evaluation of the Matrix Mittag-Leffler Function.