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)
Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations. (English) Zbl 1198.34007
Summary: We present some new existence and uniqueness results for nonlinear fractional differential equations of order q(1,2] with irregular boundary conditions in a Banach space. Our results are based on the contraction mapping principle and Krasnoselskii’s fixed point theorem.
MSC:
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
References:
[1]Ahmad, B.; Nieto, J. J.: Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Bound. value probl. (2009)
[2]Ahmad, B.; Otero-Espinar, V.: Existence of solutions for fractional differential inclusions with anti-periodic boundary conditions, Bound. value probl. (2009) · Zbl 1172.34004 · doi:10.1155/2009/625347
[3]Ahmad, B.; Sivasundaram, S.: Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions, Commun. appl. Anal. 13, 121-228 (2009) · Zbl 1180.34003
[4]Ahmad, B.; Nieto, J. J.: Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. math. Appl. 58, 1838-1843 (2009) · Zbl 1205.34003 · doi:10.1016/j.camwa.2009.07.091
[5]Chang, Y. -K.; Nieto, J. J.: Some new existence results for fractional differential inclusions with boundary conditions, Math. comput. Modelling 49, 605-609 (2009) · Zbl 1165.34313 · doi:10.1016/j.mcm.2008.03.014
[6]Gafiychuk, V.; Datsko, B.; Meleshko, V.: Mathematical modeling of time fractional reaction-diffusion systems, J. comput. Appl. math. 220, 215-225 (2008) · Zbl 1152.45008 · doi:10.1016/j.cam.2007.08.011
[7]Gejji, V. D.: Positive solutions of a system of non-autonomous fractional differential equations, J. math. Anal. appl. 302, 56-64 (2005) · Zbl 1064.34004 · doi:10.1016/j.jmaa.2004.08.007
[8]Ibrahim, R. W.; Darus, M.: Subordination and superordination for univalent solutions for fractional differential equations, J. math. Anal. appl. 345, 871-879 (2008) · Zbl 1147.30009 · doi:10.1016/j.jmaa.2008.05.017
[9]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, North-holland mathematics studies 204 (2006)
[10]Ladaci, S.; Loiseau, J. L.; Charef, A.: Fractional order adaptive high-gain controllers for a class of linear systems, Commun. nonlinear sci. Numer. simul. 13, 707-714 (2008) · Zbl 1221.93128 · doi:10.1016/j.cnsns.2006.06.009
[11]Lakshmikantham, V.; Leela, S.; Devi, J. Vasundhara: Theory of fractional dynamic systems, (2009)
[12]Podlubny, I.: Fractional differential equations, (1999)
[13]Aliyev, I.; Yakubov, S.: Solution of irregular boundary value problems of ordinary differential equations, Analysis (Munich) 21, No. 2, 135-156 (2001) · Zbl 0983.34079
[14]Bueno-Orovio, A.; Pérez-García, V. M.; Fenton, F. H.: Spectral methods for partial differential equations in irregular domains: the spectral smoothed boundary method, SIAM J. Sci. comput. 28, 886-900 (2006) · Zbl 1114.65119 · doi:10.1137/040607575
[15]Heintz, A.: On the initial boundary value problems for the Enskog equation in irregular domains, J. stat. Phys. 90, 663-695 (1998) · Zbl 0921.45006 · doi:10.1023/A:1023268718526
[16]Makin, A.: Regularized trace of the Sturm–Liouville operator with irregular boundary conditions, Electron. J. Differential equations 2009, No. 27, 1-8 (2009) · Zbl 1171.34355 · doi:emis:journals/EJDE/Volumes/2009/27/abstr.html
[17]Rashkov, R. C.: Regular and irregular boundary conditions in AdS/CFT correspondence for spinor field, Phys. lett. B 466, 190-198 (1999) · Zbl 0987.81560 · doi:10.1016/S0370-2693(99)01112-0
[18]Stupelis, L.: Navier–Stokes equations in irregular domains, (2007)
[19]Zhao, Y. B.; Wei, G. W.; Xiang, Y.: Plate vibration under irregular internal supports, Internat. J. Solids structures 39, 1361-1383 (2002) · Zbl 1090.74603 · doi:10.1016/S0020-7683(01)00241-4
[20]Smart, D. R.: Fixed point theorems, (1980)
[21]Denche, M.; Meziani, A.: Boundary-value problems for second-order differential operators with nonlocal boundary conditions, Electronic J. Differential equations 2007, No. 56 (2007) · Zbl 1131.47044 · doi:emis:journals/EJDE/Volumes/2007/56/abstr.html