Computational Methods in the Fractional Calculus of Variations

Ricardo Almeida, Shakoor Pooseh, Delfim F M Torres

• Publisher: ICP
• Year: 2015
• ISBN:
  9781783266425
• Topic: Matemáticas
• Subtopic: Análisis matemático

This book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.

The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.

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Contents:

• Introduction
• The Calculus of Variations and Optimal Control
• Fractional Calculus
• Fractional Variational Problems
• Numerical Methods for Fractional Variational Problems
• Approximating Fractional Derivatives
• Approximating Fractional Integrals
• Direct Methods
• Indirect Methods
• Fractional Optimal Control with Free End-Points
• An Expansion Formula for Fractional Operators of Variable Order
• Discrete-Time Fractional Calculus of Variations
• Conclusion

Readership: Advanced undergraduate, graduate students and researchers in mathematics, physics and applied sciences.
Key Features:

• Deals with an important subject, which has gained traction in the last two decades
• No other book deals with computational methods in fractional calculus of variations
• Serves as a good complement to A B Malinowska and D F M Torres, Introduction to the Fractional Calculus of Variations, Imperial College Press, London, 2012. That book whereas deals with the mathematical foundations of fractional variational calculus, this book is devoted to the computational aspects of the subject

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Preface
• Contents
• 1. Introduction
• 2. The calculus of variations and optimal control
• 3. Fractional calculus
• 4. Fractional variational problems
• 5. Numerical methods for fractional variational problems
• 6. Approximating fractional derivatives
• 7. Approximating fractional integrals
• 8. Direct methods
• 9. Indirect methods
• 10. Fractional optimal control with free end-points
• 11. An expansion formula for fractional operators of variable order
• 12. Discrete-time fractional calculus of variations
• 13. Conclusion
• Appendix A MATLAB® code
• Bibliography
• Index