The Variable-Order Fractional Calculus of Variations

Nonfiction, Science & Nature, Mathematics, Calculus, Technology, Engineering
Cover of the book The Variable-Order Fractional Calculus of Variations by Ricardo Almeida, Dina Tavares, 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: Ricardo Almeida, Dina Tavares, Delfim F. M. Torres ISBN: 9783319940069
Publisher: Springer International Publishing Publication: June 29, 2018
Imprint: Springer Language: English
Author: Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
ISBN: 9783319940069
Publisher: Springer International Publishing
Publication: June 29, 2018
Imprint: Springer
Language: English

​**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.

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

​**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.

More books from Springer International Publishing

Cover of the book An Algebraic Approach to Geometry by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Multilevel Network Analysis for the Social Sciences by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Culturally Responsive Pedagogy by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Complexity and Synergetics by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Graphs in Biomedical Image Analysis and Integrating Medical Imaging and Non-Imaging Modalities by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Reflected Brownian Motions in the KPZ Universality Class by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Mathematical Modeling of Disperse Two-Phase Flows by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Advances in Visual Informatics by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Acoustic Investigation of Complex Seabeds by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Being Participatory: Researching with Children and Young People by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Global Politics and Its Violent Care for Indigeneity by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Understanding Dental Caries by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Information and Communication Technology for Intelligent Systems (ICTIS 2017) - Volume 2 by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Heavily-Doped 2D-Quantized Structures and the Einstein Relation by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Metabolic Control by Ricardo Almeida, Dina Tavares, 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