Advanced Methods in the Fractional Calculus of Variations

• Main Authors: Malinowska, Agnieszka B. (Author), Odzijewicz, Tatiana (Author), Torres, Delfim F.M (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: SpringerBriefs in Applied Sciences and Technology,
• Subjects: Mathematics.; System theory.; Mathematical models.; Calculus of variations.; Physics.; Control engineering.; Economic theory.; Calculus of Variations and Optimal Control; Optimization.; Control.; Mathematical Methods in Physics.; Economic Theory/Quantitative Economics/Mathematical Methods.; Mathematical Modeling and Industrial Mathematics.; Systems Theory, Control.

This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractiona...

Table of Contents:

• 1. Introduction
• 2. Fractional Calculus
• 3. Fractional Calculus of Variations
• 4. Standard Methods in Fractional Variational Calculus
• 5. Direct Methods in Fractional Calculus of Variations
• 6. Application to the Sturm-Liouville Problem
• 7. Conclusion
• Appendix - Two Convergence Lemmas
• Index.