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)
Some results of linear fractional order time-delay system. (English) Zbl 1138.34328
Summary: We prove existence and uniqueness theorems for $$\cases D^\alpha x(t)=A_0x(t)+A_1x(t-r)+f(t),\quad & t\ge 0\\ x(t)=\phi(t),\quad t\in[-r,0],\endcases$$ Moreover, sufficient conditions for the finite time stability, for the particular class of fractional time-delay system are obtained.

MSC:
34K05General theory of functional-differential equations
34K20Stability theory of functional-differential equations
26A33Fractional derivatives and integrals (real functions)
WorldCat.org
Full Text: DOI
References:
[1] Daftardar-Gdjji, Varsha; Babakhani, A.: Analysis of a system of fractional differential equations. J. math. Anal. appl. 293, 511-522 (2004) · Zbl 1058.34002
[2] Delbosco, Domenico; Rodino, Luigi: Existence and uniqueness for a nonlinear fractional differential equation. J. math. Anal. appl. 204, 609-625 (1996) · Zbl 0881.34005
[3] Diethelm, Kai; Ford, Neville J.: Analysis of fractional differential equations. J. math. Anal. appl. 265, 229-248 (2002) · Zbl 1014.34003
[4] El-Sayed, Ahamed M. A.: On the fractional differential equations. Appl. math. Comput. 49, 205-213 (1992) · Zbl 0757.34005
[5] El-Sayed, Ahamed M. A.: Fractional order differential equation. Kyungpook math. J. 28 (1988)
[6] El-Sayed, Ahamed M. A.: Nonlinear functional differential equations of arbitrary orders. Nonlinear anal. 33, No. 2, 181-186 (1998) · Zbl 0934.34055
[7] Yu, Cheng; Gao, Guozhu: Some results on a class of fractional functional differential equations. Commun. appl. Nonlinear anal. 11, No. 3, 67-75 (2004) · Zbl 1051.34048
[8] Hale, Jack: Theory of functional differential equations. (1997)
[9] Lazarević, M. P.: Finite time stability analysis of PD$\alpha $ fractional control of robotic time-delay systems. Mech. res. Commun. 33, 269-279 (2006) · Zbl 1192.70008
[10] Podlubny, I.: Fractional differential equations. (1999) · Zbl 0924.34008
[11] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equation. (1993) · Zbl 0789.26002
[12] Daftardar-Gejji, Varsha: Positive solutions of a system of a nonautomous fractional differential equations. J. math. Anal. appl. 302, 56-64 (2005) · Zbl 1064.34004