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)
Global attractivity for nonlinear fractional differential equations. (English) Zbl 1238.34011
Summary: We present some results for the global attractivity of solutions for fractional differential equations involving Riemann-Liouville fractional calculus. The results are obtained by employing Krasnoselskii’s fixed point theorem. Similar results for fractional differential equations involving Caputo fractional derivative are also obtained by using the classical Schauder’s fixed point theorem. Several examples are given to illustrate our main results.
MSC:
34A08Fractional differential equations
References:
[1]Podlubny, I.: Fractional differential equation, (1999)
[2]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[3]Agarwal, Ravi P.; Benchohra, M.; Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta appl. Math. 109, 973-1033 (2010) · Zbl 1198.26004 · doi:10.1007/s10440-008-9356-6
[4]Agarwal, R. P.; Lakshmikantham, V.; Nieto, J. J.: On the concept of solution for fractional differential equations with uncertainty, Nonlinear anal. 72, 2859-2862 (2009) · Zbl 1188.34005 · doi:10.1016/j.na.2009.11.029
[5]Agarwal, R. P.; O’regan, D.; Staněk, S.: Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations, J. math. Anal. appl. 371, 57-68 (2010) · Zbl 1206.34009 · doi:10.1016/j.jmaa.2010.04.034
[6]Agarwal, R. P.; Zhou, Y.; He, Y.: Existence of fractional neutral functional differential equations, Comput. math. Appl. 59, 1095-1100 (2010) · Zbl 1189.34152 · doi:10.1016/j.camwa.2009.05.010
[7]Arara, A.: Fractional order differential equations on an unbounded domain, Nonlinear anal. 72, 580-586 (2010)
[8]Chang, Y. K.; Nieto, J. J.: Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators, Numer. funct. Anal. optim. 30, 227-244 (2009) · Zbl 1176.34096 · doi:10.1080/01630560902841146 · doi:http://www.informaworld.com/smpp/./content~db=all~content=a910367252
[9]Belmekki, M.; Nieto, Juan J.; Rodríguez-López, R.: Existence of periodic solution for a nonlinear fractional differential equation, Bound. value probl. (2009) · Zbl 1181.34006 · doi:10.1155/2009/324561
[10]El-Shahed, M.; Nieto, J. J.: Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order, Comput. math. Appl. 59, 3438-3443 (2010) · Zbl 1197.34003 · doi:10.1016/j.camwa.2010.03.031
[11]Jumarie, G.: Fractional multiple birth-death processes with birth probabilities λi(δt)α+o((δt)α), J. franklin inst. 347, 1797-1942 (2010) · Zbl 1225.60141 · doi:10.1016/j.jfranklin.2010.09.004
[12]Nieto, J. J.: Maximum principles for fractional differential equations derived from Mittag-Leffler functions, Appl. math. Lett. 23, 1248-1251 (2010) · Zbl 1202.34019 · doi:10.1016/j.aml.2010.06.007
[13]Li, C. F.; Luo, X. N.; Zhou, Y.: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Comput. math. Appl. 59, 1363-1375 (2010) · Zbl 1189.34014 · doi:10.1016/j.camwa.2009.06.029
[14]Zhou, Y.; Jiao, F.; Li, J.: Existence and uniqueness for fractional neutural differential equations with infinite delay, Nonlinear anal. 71, 3249-3256 (2009) · Zbl 1177.34084 · doi:10.1016/j.na.2009.01.202
[15]Zhou, Y.: Existence and uniqueness of solutions for a system of fractional differential equations, Fract. calc. Appl. anal. 12, 195-204 (2009)
[16]Wang, J.; Zhou, Y.: A class of fractional evolution equations and optimal controls, Nonlinear anal. RWA 12, 262-272 (2011) · Zbl 1214.34010 · doi:10.1016/j.nonrwa.2010.06.013
[17]Sabatier, J.; Moze, M.; Farges, C.: LMI stability conditions for fractional order systems, Comput. math. Appl. 59, 1594-1609 (2010) · Zbl 1189.34020 · doi:10.1016/j.camwa.2009.08.003
[18]Burton, T. A.; Furumochi, T.: Krasnoselskii’s fixed point theorem and stability, Nonlinear anal. 49, 445-454 (2002) · Zbl 1015.34046 · doi:10.1016/S0362-546X(01)00111-0
[19]Raffoul, Y. N.: Stability in neutral nonlinear differential equations with functional delays using fixed-point theory, Math. comput. Modelling 44, 691-700 (2004) · Zbl 1083.34536 · doi:10.1016/j.mcm.2004.10.001
[20]Burton, T. A.: Fixed points, stability, and exact linearization, Nonlinear anal. 61, 857-870 (2005) · Zbl 1067.34077 · doi:10.1016/j.na.2005.01.079
[21]Jin, C.; Luo, J.: Stability in functional differential equations established using fixed point theory, Nonlinear anal. 68, 3307-3315 (2008) · Zbl 1165.34042 · doi:10.1016/j.na.2007.03.017
[22]Krasnoselskii, M. A.: Topological methods in the theory of nonlinear integral equations, (1964) · Zbl 0111.30303
[23]Burton, T. A.: A fixed point theorem of Krasnoselskii, Appl. math. Lett. 11, 85-88 (1998) · Zbl 1127.47318 · doi:10.1016/S0893-9659(97)00138-9
[24]Hale, J. K.: Theory of function differential equations, (1977)