The Variable-Order Fractional Calculus of Variations - Ricardo Almeida, Dina Tavares, Delfim F. M. Torres

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The Variable-Order Fractional Calculus of Variations (eBook)

Ricardo Almeida, Dina Tavares, Delfim F. M. Torres (Autoren)

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2018 | 1st ed. 2019
XIV, 124 Seiten
Springer International Publishing (Verlag)
978-3-319-94006-9 (ISBN)

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The Variable-Order Fractional Calculus of Variations is devoted to the study of fractional operators with variable order and, in particular, variational problems involving variable-order operators. This brief presents a new numerical tool for the solution of differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one, an approximation formula is obtained in terms of standard (integer-order) derivatives only. Estimations for the error of the approximations are also provided.

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.

Ricardo Almeida received his Bachelor and Master degrees in Mathematics from University of Porto, Portugal, and

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.

Ricardo Almeida received his Bachelor and Master degrees in Mathematics from University of Porto, Portugal, andhis Ph.D. degree in Mathematics from University of Aveiro, Portugal. He is currently an Assistant Professor in theUniversity of Aveiro. His research interests include fractional calculus, calculus of variations and optimal controltheory. 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 variationsand mathematics education.Delfim F.M. Torres is a Full Professor of Mathematics at the University of Aveiro since 2015 and Coordinator of theSystems 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 CitedResearcher. He has written more than 400 publications, including two books with Imperial College Press, in 2012and 2015, and two books with Springer, in 2014 and 2015. He is the Director of the FCT Doctoral Program ofExcellence in Mathematics and Applications of Universities of Minho, Aveiro, Porto and UBI since 2013. SixteenPhD students in mathematics (six of which woman) have successfully finished under his supervision.

Fractional Calculus.- The Calculus of Variations.- Expansion Formulas for Fractional Derivatives.- The Fractional Calculus of Variations.

Erscheint lt. Verlag	29.6.2018
Reihe/Serie	SpringerBriefs in Applied Sciences and Technology
Zusatzinfo	XIV, 124 p. 12 illus., 11 illus. in color.
Verlagsort	Cham
Sprache	englisch
Themenwelt	Technik
Schlagworte	error estimation • Fractional Calculus • Fractional Calculus of Variations • Fractional Necessary Optimality Conditions • numerical approximation • Transversality Conditions
ISBN-10	3-319-94006-6 / 3319940066
ISBN-13	978-3-319-94006-9 / 9783319940069

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