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010   $a3-319-94006-6
024 7 $a10.1007/978-3-319-94006-9
035   $a(CKB)3850000000036109
035   $a(DE-He213)978-3-319-94006-9
035   $a(MiAaPQ)EBC5596977
035   $a(PPN)229495702
035   $a(EXLCZ)993850000000036109
100   $a20180629d2019      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 14$aThe Variable-Order Fractional Calculus of Variations /$fby Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
205   $a1st ed. 2019.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019.
215   $a1 online resource (XIV, 124 p. 12 illus., 11 illus. in color.) 
225 1 $aSpringerBriefs in Applied Sciences and Technology,$x2191-530X
311   $a3-319-94005-8 
320   $aIncludes bibliographical references and index.
327   $aFractional Calculus -- The Calculus of Variations -- Expansion Formulas for Fractional Derivatives -- The Fractional Calculus of Variations.
330   $aThe Variable-Order Fractional Calculus of Variations is devoted to the study of fractional operators with variable order and, in particular, variational problems involving variable-order operators. This brief presents a new numerical tool for the solution of differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one, an approximation formula is obtained in terms of standard (integer-order) derivatives only. Estimations for the error of the approximations are also provided. The contributors consider variational problems that may be subject to one or more constraints, where the functional depends on a combined Caputo derivative of variable fractional order. In particular, they establish necessary optimality conditions of Euler?Lagrange type. As the terminal point in the cost integral is free, as is the terminal state, transversality conditions are also obtained. The Variable-Order Fractional Calculus of Variations is a valuable source of information for researchers in mathematics, physics, engineering, control and optimization; it provides both analytical and numerical methods to deal with variational problems. It is also of interest to academics and postgraduates in these fields, as it solves multiple variational problems subject to one or more constraints in a single brief.
410  0$aSpringerBriefs in Applied Sciences and Technology,$x2191-530X
606   $aEngineering mathematics
606   $aCalculus of variations
606   $aCalculus
606   $aEngineering Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/T11030
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
606   $aCalculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12220
615  0$aEngineering mathematics.
615  0$aCalculus of variations.
615  0$aCalculus.
615 14$aEngineering Mathematics.
615 24$aCalculus of Variations and Optimal Control; Optimization.
615 24$aCalculus.
676   $a515.83
700   $aAlmeida$b Ricardo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0873947
702   $aTavares$b Dina$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aTorres$b Delfim F. M$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910337603503321
996   $aThe Variable-Order Fractional Calculus of Variations$91951170
997   $aUNINA