zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A formulation of Noether’s theorem for fractional problems of the calculus of variations. (English) Zbl 1119.49035
The authors extend classical results from calculus of variations to the context of fractional differentiation. They use the notion of Euler-Lagrange fractional extremal in order to extend a Noether-type theorem to problems having fractional derivatives. They also propose a generalization of the classical concept of conservation law. In their analysis, the authors use the results from [{\it O. P. Agrawal}, J. Math. Anal. Appl. 272, No. 1, 368--379 (2002; Zbl 1070.49013)].

49S05Variational principles of physics
26A33Fractional derivatives and integrals (real functions)
70S10Symmetries and conservation laws
Full Text: DOI arXiv
[1] Agrawal, O. P.: Formulation of Euler -- Lagrange equations for fractional variational problems. J. math. Anal. appl. 272, No. 1, 368-379 (2002) · Zbl 1070.49013
[2] Agrawal, O. P.: A general formulation and solution scheme for fractional optimal control problems. Nonlinear dynam. 38, No. 1 -- 4, 323-337 (2004) · Zbl 1121.70019
[3] Agrawal, O. P.; Machado, J. A. Tenreiro; Sabatier, J.: Introduction. Nonlinear dynam. 38, No. 1 -- 4, 1-2 (2004)
[4] Baleanu, D.; Avkar, Tansel: Lagrangians with linear velocities within Riemann -- Liouville fractional derivatives. Nuovo cimento 119, 73-79 (2004)
[5] Gouveia, P. D. F.; Torres, D. F. M.: Automatic computation of conservation laws in the calculus of variations and optimal control. Comput. methods appl. Math. 5, No. 4, 387-409 (2005) · Zbl 1079.49019
[6] Hilfer, R.: Applications of fractional calculus in physics. (2000) · Zbl 0998.26002
[7] Jost, J.; Li-Jost, X.: Calculus of variations. (1998) · Zbl 0913.49001
[8] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations. North-holland math. Stud. 204 (2006)
[9] Klimek, M.: Stationarity-conservation laws for fractional differential equations with variable coefficients. J. phys. A 35, No. 31, 6675-6693 (2002) · Zbl 1039.35005
[10] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations. (1993) · Zbl 0789.26002
[11] Muslih, S. I.; Baleanu, D.: Hamiltonian formulation of systems with linear velocities within Riemann -- Liouville fractional derivatives. J. math. Anal. appl. 304, No. 2, 599-606 (2005) · Zbl 1149.70320
[12] Riewe, F.: Nonconservative Lagrangian and Hamiltonian mechanics. Phys. rev. E (3) 53, No. 2, 1890-1899 (1996)
[13] Riewe, F.: Mechanics with fractional derivatives. Phys. rev. E (3) 55, No. 3, 3581-3592 (1997)
[14] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives --- theory and applications. (1993)
[15] Torres, D. F. M.: On the Noether theorem for optimal control. Eur. J. Control 8, No. 1, 56-63 (2002) · Zbl 1293.49051
[16] Torres, D. F. M.: Quasi-invariant optimal control problems. Port. math. (N.S.) 61, No. 1, 97-114 (2004) · Zbl 1042.49015
[17] Torres, D. F. M.: Proper extensions of Noether’s symmetry theorem for nonsmooth extremals of the calculus of variations. Comm. pure appl. Anal. 3, No. 3, 491-500 (2004) · Zbl 1058.49019