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 Micromechanics of Materials, with Applications by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Small-Gauge Vitrectomy for Diabetic Retinopathy by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book From Classical to Modern Analysis by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Extended Abstracts Fall 2012 by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Service Systems by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Computer Science – Theory and Applications by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Artificial Economics and Self Organization by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Legal Personhood: Animals, Artificial Intelligence and the Unborn by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Illness, Identity, and Taboo among Australian Paleo Dieters by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book The Social Life of Memory by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book The Automotive Transmission Book by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Progress in Approximation Theory and Applicable Complex Analysis by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Mental Health and Older People by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Quantum Walks and Search Algorithms by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
Cover of the book Galactic and Intergalactic Magnetic Fields 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