Overview
- Provides a numerical approach to deal with fractional problems of variable order
- Contains recent developments on the theory of fractional variational calculus
- Establishes necessary optimality conditions of Euler-Lagrange type
Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (4 chapters)
Keywords
About this book
The contributors consider variational problems that may be subject to one or more constraints, where the functional depends on a combined Caputo derivative of variable fractional order. In particular, they establish necessary optimality conditions of Euler–Lagrange type. As the terminal point in the cost integral is free, as is the terminal state, transversality conditions are also obtained.
The Variable-Order Fractional Calculus of Variations is a valuable source of information for researchers in mathematics, physics, engineering, control and optimization; it provides both analytical and numerical methods to deal with variational problems. It is also of interest to academics and postgraduates in these fields, as it solves multiple variational problems subject to one or more constraints in a single brief.
Authors and Affiliations
About the authors
his Ph.D. degree in Mathematics from University of Aveiro, Portugal. He is currently an Assistant Professor in the
University of Aveiro. His research interests include fractional calculus, calculus of variations and optimal control
theory. Ricardo Almeida has written 4 books and more than 60 publications in international journals.
Dina Tavares obtained her Master and PhD degrees in Mathematics from University of Aveiro. She is an Adjunct Professor at the School of Education and Social Sciences (ESECS) of Polytechnic Institute of Leiria (IPL), Portugal, since 2017. Her research interests include fractional calculus, calculus of variations
and mathematics education.
Delfim F.M. Torres is a Full Professor of Mathematics at the University of Aveiro since 2015 and Coordinator of the
Systems and Control Group of CIDMA since 2010. He obtained PhD in Mathematics in 2002 and DSc (Habilitation)
in Mathematics in 2011. Professor Torres has been awarded in 2015, 2016 and 2017 with the title of ISI Highly Cited
Researcher. He has written more than 400 publications, including two books with Imperial College Press, in 2012
and 2015, and two books with Springer, in 2014 and 2015. He is the Director of the FCT Doctoral Program of
Excellence in Mathematics and Applications of Universities of Minho, Aveiro, Porto and UBI since 2013. Sixteen
PhD students in mathematics (six of which woman) have successfully finished under his supervision.
Bibliographic Information
Book Title: The Variable-Order Fractional Calculus of Variations
Authors: Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Series Title: SpringerBriefs in Applied Sciences and Technology
DOI: https://doi.org/10.1007/978-3-319-94006-9
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-319-94005-2Published: 09 July 2018
eBook ISBN: 978-3-319-94006-9Published: 29 June 2018
Series ISSN: 2191-530X
Series E-ISSN: 2191-5318
Edition Number: 1
Number of Pages: XIV, 124
Number of Illustrations: 1 b/w illustrations, 11 illustrations in colour
Topics: Engineering Mathematics, Calculus of Variations and Optimal Control; Optimization, Calculus