zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Formulation of Euler-Lagrange equations for fractional variational problems. (English) Zbl 1070.49013
The author gives an analogue of the Euler equation for the variational problem for the functional $J[y]= \int_a^b F(x,y,y^{(\alpha)}_+, y^{(\beta)}_-)\; dx$ where $y^{(\alpha)}_+$ and $ y^{(\beta)}_-$ stand, respectively, for the left-hand sided and right-hand sided fractional derivatives.

MSC:
49K05Free problems in one independent variable (optimality conditions)
26A33Fractional derivatives and integrals (real functions)
WorldCat.org
Full Text: DOI
References:
[1] Bliss, G. A.: Lectures on the calculus of variations. (1963)
[2] Gelfand, I. M.; Fomin, S. V.: Calculus of variations. (1963) · Zbl 0127.05402
[3] Weinstock, R.: Calculus of variations with applications to physics and engineering. (1974) · Zbl 0296.49001
[4] Dym, C. L.; Shames, I. H.: Solid mechanics: A variational approach. (1973) · Zbl 1279.74001
[5] Hestenes, M. R.: Calculus of variations and optimal control theory. (1966) · Zbl 0173.35703
[6] Gregory, J.; Lin, C.: Constrained optimization in the calculus of variations and optimal control theory. (1992) · Zbl 0822.49001
[7] Agrawal, O. P.; Gregory, J.; Spector, K. P.: A bliss-type multiplier rule for constrained variational problems with time delay. J. math. Anal. appl. 210, 702-711 (1997) · Zbl 0903.49004
[8] Reddy, J. N.: Energy and variational methods in applied mechanics: with an introduction to the finite element method. (1984) · Zbl 0635.73017
[9] Riewe, F.: Nonconservative Lagrangian and Hamiltonian mechanics. Phys. rev. E 53, 1890-1899 (1996)
[10] Riewe, F.: Mechanics with fractional derivatives. Phys. rev. E 55, 3582-3592 (1997)
[11] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations. (1993) · Zbl 0789.26002
[12] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives--theory and applications. (1993) · Zbl 0818.26003
[13] Oldham, K. B.; Spanier, J.: The fractional calculus. (1974) · Zbl 0292.26011
[14] Gorenflo, R.; Mainardi, F.: Fractional calculus: integral and differential equations of fractional order. Fractals and fractional calculus in continuum mechanics, 223-276 (1997)
[15] Mainardi, F.: Fractional calculus: some basic problems in continuum and statistical mechanics. Fractals and fractional calculus in continuum mechanics, 291-348 (1997) · Zbl 0917.73004
[16] Podlubny, I.: Fractional differential equations. (1999) · Zbl 0924.34008
[17] Butzer, P. L.; Westphal, U.: An introduction to fractional calculus. Applications of fractional calculus in physics, 1-85 (2000) · Zbl 0987.26005
[18] Bagley, R. L.; Torvik, P. J.: On the fractional calculus model of viscoelastic behavior. J. rheology 30, 133-155 (1986) · Zbl 0613.73034