The Variable-Order Fractional Calculus of Variations

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 d...

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Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Almeida, Ricardo (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Tavares, Dina (http://id.loc.gov/vocabulary/relators/aut), Torres, Delfim F. M. (http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
Έκδοση:1st ed. 2019.
Σειρά:SpringerBriefs in Applied Sciences and Technology,
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Almeida, Ricardo.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 4 |a The Variable-Order Fractional Calculus of Variations  |h [electronic resource] /  |c by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres. 
250 |a 1st ed. 2019. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2019. 
300 |a XIV, 124 p. 12 illus., 11 illus. in color.  |b online resource. 
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490 1 |a SpringerBriefs in Applied Sciences and Technology,  |x 2191-530X 
505 0 |a Fractional Calculus -- The Calculus of Variations -- Expansion Formulas for Fractional Derivatives -- The Fractional Calculus of Variations. 
520 |a 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. 
650 0 |a Engineering mathematics. 
650 0 |a Calculus of variations. 
650 0 |a Calculus. 
650 1 4 |a Engineering Mathematics.  |0 http://scigraph.springernature.com/things/product-market-codes/T11030 
650 2 4 |a Calculus of Variations and Optimal Control; Optimization.  |0 http://scigraph.springernature.com/things/product-market-codes/M26016 
650 2 4 |a Calculus.  |0 http://scigraph.springernature.com/things/product-market-codes/M12220 
700 1 |a Tavares, Dina.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Torres, Delfim F. M.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
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776 0 8 |i Printed edition:  |z 9783319940052 
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950 |a Engineering (Springer-11647)