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008 180629s2019 sz | s |||| 0|eng d
020 _a9783319940069
_9978-3-319-94006-9
024 7 _a10.1007/978-3-319-94006-9
_2doi
050 4 _aTA329-348
072 7 _aTBJ
_2bicssc
072 7 _aTEC009000
_2bisacsh
072 7 _aTBJ
_2thema
082 0 4 _a620.00151
_223
100 1 _aAlmeida, Ricardo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_955039
245 1 4 _aThe Variable-Order Fractional Calculus of Variations
_h[electronic resource] /
_cby Ricardo Almeida, Dina Tavares, Delfim F. M. Torres.
250 _a1st ed. 2019.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2019.
300 _aXIV, 124 p. 12 illus., 11 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Applied Sciences and Technology,
_x2191-5318
505 0 _aFractional Calculus -- The Calculus of Variations -- Expansion Formulas for Fractional Derivatives -- The Fractional Calculus of Variations.
520 _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.
650 0 _aEngineering mathematics.
_93254
650 0 _aMathematical optimization.
_94112
650 0 _aCalculus of variations.
_917382
650 0 _aMathematical analysis.
_911486
650 1 4 _aEngineering Mathematics.
_93254
650 2 4 _aCalculus of Variations and Optimization.
_931596
650 2 4 _aIntegral Transforms and Operational Calculus.
_939156
700 1 _aTavares, Dina.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_955040
700 1 _aTorres, Delfim F. M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_955041
710 2 _aSpringerLink (Online service)
_955042
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319940052
776 0 8 _iPrinted edition:
_z9783319940076
830 0 _aSpringerBriefs in Applied Sciences and Technology,
_x2191-5318
_955043
856 4 0 _uhttps://doi.org/10.1007/978-3-319-94006-9
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c79477
_d79477