Advanced Methods in the Fractional Calculus of Variations

Nonfiction, Science & Nature, Technology, Automation, Mathematics, Calculus
Cover of the book Advanced Methods in the Fractional Calculus of Variations by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres ISBN: 9783319147567
Publisher: Springer International Publishing Publication: February 5, 2015
Imprint: Springer Language: English
Author: Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
ISBN: 9783319147567
Publisher: Springer International Publishing
Publication: February 5, 2015
Imprint: Springer
Language: English

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 fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm–Liouville problems.

Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm–Liouville problems.

Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.

More books from Springer International Publishing

Cover of the book The Solar System in Close-Up by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Applications of EPR in Radiation Research by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Modelling of Magmatic and Allied Processes by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Security and Privacy in Communication Networks by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Agile Project Management: Managing for Success by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Sustainable Ecological Engineering Design by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Compact Representations for the Design of Quantum Logic by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Symbolic and Quantitative Approaches to Reasoning with Uncertainty by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Proceedings of the 5th International Conference on Jets, Wakes and Separated Flows (ICJWSF2015) by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Visibility-based Optimal Path and Motion Planning by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book On the Move to Meaningful Internet Systems. OTM 2018 Conferences by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Landscape Analysis and Planning by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book The Musical-Mathematical Mind by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Modern Statistical Methods for HCI by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
Cover of the book Biopsy Diagnosis of Peripheral Neuropathy by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy