國立虎尾科技大學 |

The Variable-Order Fractional Calculus of Variations

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Variable-Order Fractional Calculus of Variations/ by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres.
作者:	Almeida, Ricardo.
其他作者:	Tavares, Dina.
面頁冊數:	XIV, 124 p. 12 illus., 11 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Engineering mathematics. -
電子資源:	https://doi.org/10.1007/978-3-319-94006-9
ISBN:	9783319940069

The Variable-Order Fractional Calculus of Variations
Almeida, Ricardo.

The Variable-Order Fractional Calculus of Variations[electronic resource] /by Ricardo Almeida, Dina Tavares, Delfim F. M. Torres. - 1st ed. 2019. - XIV, 124 p. 12 illus., 11 illus. in color.online resource. - SpringerBriefs in Applied Sciences and Technology,2191-530X. - SpringerBriefs in Applied Sciences and Technology,.

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

ISBN: 9783319940069

Standard No.: 10.1007/978-3-319-94006-9doiSubjects--Topical Terms:

562757
Engineering mathematics.

LC Class. No.: TA329-348

Dewey Class. No.: 620.00151

The Variable-Order Fractional Calculus of Variations
LDR:02930nam a22003975i 4500 001 1016484
003 DE-He213
005 20200705032204.0
007 cr nn 008mamaa
008 210106s2019 gw | s |||| 0|eng d
020 $a 9783319940069 $9 978-3-319-94006-9
024 7 $a 10.1007/978-3-319-94006-9 $2 doi
035 $a 978-3-319-94006-9
050 4 $a TA329-348
072 7 $a TBJ $2 bicssc
072 7 $a TEC009000 $2 bisacsh
072 7 $a TBJ $2 thema
082 0 4 $a 620.00151 $2 23
100 1 $a Almeida, Ricardo. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1225859
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.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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. $3 562757
650 0 $a Calculus of variations. $3 527927
650 0 $a Calculus. $3 672391
650 1 4 $a Engineering Mathematics. $3 1203947
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
700 1 $a Tavares, Dina. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1310907
700 1 $a Torres, Delfim F. M. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1310908
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319940052
776 0 8 $i Printed edition: $z 9783319940076
830 0 $a SpringerBriefs in Applied Sciences and Technology, $x 2191-530X $3 1253575
856 4 0 $u https://doi.org/10.1007/978-3-319-94006-9
912 $a ZDB-2-ENG
912 $a ZDB-2-SXE
950 $a Engineering (SpringerNature-11647)
950 $a Engineering (R0) (SpringerNature-43712)