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)
Higher order fractional variational optimal control problems with delayed arguments. (English) Zbl 1244.49028
Summary: This article deals with higher order Caputo fractional variational problems in the presence of delay in the state variables and their integer higher order derivatives.
MSC:
49J99Existence theory for optimal solutions
26A33Fractional derivatives and integrals (real functions)
References:
[1]Kilbas, A. A.; Srivastava, H. H.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[2]Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives – theory and applications, (1993) · Zbl 0818.26003
[3]Magin, R. L.: Fractional calculus in bioengineering, (2006)
[4]Heymans, N.; Podlubny, I.: Physical interpretation of initial conditions for fractional differential equations with Riemann – Liouville fractional derivatives, Rheol. acta 45, 765-771 (2006)
[5]Jesus, I. S.; Machado, J. A. T.: Fractional control of heat diffusion system, Nonlinear dynam. 54, No. 3, 263-282 (2008) · Zbl 1210.80008 · doi:10.1007/s11071-007-9322-2
[6]Baleanu, D.; Maraaba, T.; Jarad, F.: Fractional principles with delay, J. phys. A: math. Theor. 41 (2008)
[7]Jarad, F.; Maraaba, T.; Baleanu, D.: Fractional variational principles with delay within Caputo derivatives, Rep. math. Phys. 65, No. 1, 17-28 (2010) · Zbl 1195.49030 · doi:10.1016/S0034-4877(10)00010-8
[8]Mainardi, F.; Luchko, Y.; Pagnini, G.: The fundamental solution of the space-time fractional the space-time fractional diffusion equation, Frac. calc. Appl. anal. 4, No. 2, 153-192 (2001) · Zbl 1054.35156
[9]Scalas, E.; Gorenflo, R.; Mainardi, F.: Uncoupled continuous-time random walks: solution and limiting behavior of the master equation, Phys. rev. E 69, 011107-1 (2004)
[10]Li, C. P.; Zhao, Z. G.: Introduction to fractional integrability and differentiability, Eur. phys. J. special topics 193, 5-26 (2011)
[11]Agrawal, O. P.; Baleanu, D.: Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems, J. vib. Control 13, No. 9 – 10, 1269-1281 (2007) · Zbl 1182.70047 · doi:10.1177/1077546307077467
[12]Chen, Y. Q.; Vinagre, B. M.; Podlubny, I.: Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review, Nonlinear dynam. 38, No. 1 – 4, 155-170 (2004) · Zbl 1134.93300 · doi:10.1007/s11071-004-3752-x
[13]Rosenblueth, J. F.: Systems with time delay in the calculus of variations: a variational approach, J. math. Control inf. 5, No. 2, 125-145 (1988) · Zbl 0655.49017 · doi:10.1093/imamci/5.2.125
[14]Tarasov, V. E.; Zaslavsky, G. M.: Nonholonomic constraints with fractional derivatives, J. phys. A: math. Gen. 39, No. 31, 9797-9815 (2006) · Zbl 1101.70011 · doi:10.1088/0305-4470/39/31/010
[15]Agrawal, O. P.: A general formulation and solution scheme for fractional optimal control problems, Nonlinear dynam. 38, 323-337 (2004) · Zbl 1121.70019 · doi:10.1007/s11071-004-3764-6