Advanced Methods in the Fractional Calculus of Variations / SpringerBriefs in Applied Sciences and Technology (PDF)
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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.
Tatiana Odzijewicz is a Post-doc Researcher at the Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, Portugal. She received M.Sc. from University of Bialystok, Poland (2009) and PhD in Mathematics and Applications from University of Aveiro, Portugal (2013). Her research is mainly in fractional calculus, generalized operators, the calculus of variations and optimal control. Tatiana Odzijewicz has been recipient, in 2012, of the celebrated Grunvald-Letnikov Award.
Delfim F. M. Torres was born August 16, 1971, in Nampula, Mozambique. He is currently an Associate Professor with Habilitation at the Department of Mathematics, University of Aveiro (UA), Portugal; Coordinator of the group on Mathematical Theory of Systems and Control of the Center for Research and Development in Mathematics and Applications (CIDMA); Director of The FCT Doctoral Program in Mathematics and Applications (FCT MAP-PDMA) of the Universities of Minho, Aveiro, Porto and UBI, Portugal; Editor-in-Chief of the Int. J. Appl. Math. Stat. (IJAMAS) since 2008;
Delfim F. M. Torres has written about 300 scientific and pedagogical publications, including research papers in first class international journals, refereed conference proceedings, chapters in books and books (as author and also as an editor). In particular, he has co-authored a book about the Fractional Calculus of Variations with Imperial College Press and World Scientific Publishing, 2012, a book on Quantum Variational Calculus with Springer, 2014 and 56 papers in international journals ranked in the 1st quartile by ISI Web of Science, according with the Journal Citation Reports Science Edition as released in 2013. Delfim F. M. Torres has 20 years of excellent teaching experience both to undergraduate and postgraduate students on Mathematics and Science and Engineering, in Portugal and abroad. He has held several positions of Invited Professor in Europe, Africa, and USA. He is a member of Scientific Committees and invited plenary speaker at several international conferences. His current research interests include several topics in the areas of the Calculus of Variations and Optimal Control, Fractional Calculus and Time Scales and its connections with the Mathematical Theory of Control, Optimization, Epidemiology and Mathematical Physics.
- Autoren: Agnieszka B. Malinowska , Tatiana Odzijewicz , Delfim F. M. Torres
- 2015, 2015, 135 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319147560
- ISBN-13: 9783319147567
- Erscheinungsdatum: 05.02.2015
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