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)
On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives. (English) Zbl 1179.26024
Summary: Local and global existence and uniqueness theorems for a functional delay fractional differential equation with bounded delay are investigated. The continuity with respect to the initial function is proved under Lipschitz and the continuity kind conditions are analyzed.
MSC:
26A33Fractional derivatives and integrals (real functions)
References:
[1]Podlubny I. Fractional Differential Equations. San Diego: Academic Press, 1999
[2]Kilbas A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations. In: North-Holland Mathematicas Studies, Vol 204. New Zealand: Elsevier, 2006
[3]Heymans N, Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheol Acta, 45: 765–771 (2006) · doi:10.1007/s00397-005-0043-5
[4]Mainardi F. Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Solitons Fractals, 7(9): 1461–1477 (1996) · Zbl 1080.26505 · doi:10.1016/0960-0779(95)00125-5
[5]Kilbas A A, Rivero M, Trujillo J J. Existence and uniqueness theorems for differential equations of fractional order in weighted spaces of continuous functions. Frac Calc Appl Anal, 6(4): 363–400 (2003)
[6]Silva M F, Machado J A T, Lopes A M. Modelling and simulation of artificial locomotion systems. Robotica, 23: 595–606 (2005) · doi:10.1017/S0263574704001195
[7]Agrawal O P, Baleanu D. A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems. J Vib Control, 13(9–10): 1269–1281 (2007) · Zbl 1182.70047 · doi:10.1177/1077546307077467
[8]Scalas E. Mixtures of compound Poisson processes as models of tick-by-tick financial data. Chaos Solitons Fractals, 34(1): 33–40 (2007) · Zbl 1142.60392 · doi:10.1016/j.chaos.2007.01.047
[9]Chen W. A speculative study of 2/3-order fractional Laplacian modelling of turbulence: some thoughts and conjectures. Chaos, 16(2): 1–11 (2006)
[10]Riewe F. Nonconservative Lagrangian and Hamiltonian mechanics. Phys Rev E, 53: 1890–1899 (1996) · doi:10.1103/PhysRevE.53.1890
[11]Klimek M. Fractional sequential mechanics-models with symmetric fractional derivatives. Czech J Phys, 51: 1348–1354 (2001) · Zbl 1064.70507 · doi:10.1023/A:1013378221617
[12]Agrawal O P. Formulation of Euler-Lagrange equations for fractional variational problems. J Math Anal Appl, 272: 368–379 (2002) · Zbl 1070.49013 · doi:10.1016/S0022-247X(02)00180-4
[13]Baleanu D. Fractional Hamiltoian analysis of irregular systems. Signal Processing, 86(10): 2632–2636 (2006) · Zbl 1172.94362 · doi:10.1016/j.sigpro.2006.02.008
[14]Baleanu D, Muslih S I. Formulation of Hamiltonian equations for fractional variational problems. Czech J Phys, 55(6): 633–642 (2005) · Zbl 1181.70017 · doi:10.1007/s10582-005-0067-1
[15]Baleanu D, Muslih S I. Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives. Physica Scripta, 72(2–3): 119–121 (2005) · Zbl 1122.70360 · doi:10.1238/Physica.Regular.072a00119
[16]Baleanu D, Muslih S I, Tas K. Fractional Hamiltonian analysis of higher order derivatives systems. J Math Phys, 47(10): 103503 (2006) · Zbl 1112.81074 · doi:10.1063/1.2356797
[17]Driver R D. Ordinary and delay differential equations. In: Applied Mathematical Sciences. New York: Springer-Verlag, 1977
[18]Deng W, Li C, Lu J. Stability analysis of linear fractional differential system with multiple time scales. Nonlinear Dynam, 48: 409–416 (2007) · Zbl 1185.34115 · doi:10.1007/s11071-006-9094-0
[19]Diethelm K, Ford N J, Freed A D, Luchko Y. Algorithms for the fractional calculus: A selection of numerical methods. Comput Methods Appl Mech Engrg, 194(6–8): 743–773 (2005) · Zbl 1119.65352 · doi:10.1016/j.cma.2004.06.006
[20]Podlubny I. Fractional derivatives: History, Theory, Application, Symposium on applied fractional calculus. Badajos, Spain, October 17–20, 2007