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)
Positive solutions for boundary value problems of nonlinear fractional differential equations. (English) Zbl 1227.34011
The existence of at least one or two positive solutions for boundary eigenvalue problems of nonlinear fractional differential equations is established by using properties of the Green function and the Guo-Krasnosel’skii fixed point theorem on cones.
MSC:
34A08Fractional differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
34B09Boundary eigenvalue problems for ODE
47N20Applications of operator theory to differential and integral equations
References:
[1]Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equation, (1993)
[2]Oldham, K. B.; Spanier, J.: The fractional calculus, (1974)
[3]Podlubny, I.: Fractional differential equations, (1999)
[4]Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integral and derivative, (1993)
[5]Agarwal, R. 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
[6]Agarwal, R. P.; Belmekki, Mohammed; Benchohra, Mouffak: A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative, Advances in difference equations 2009, 47 (2009) · Zbl 1182.34103 · doi:10.1155/2009/981728
[7]Delbosco, D.; Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equation, J. math. Anal. appl. 204, 609-625 (1996) · Zbl 0881.34005 · doi:10.1006/jmaa.1996.0456
[8]Zhang, S.: The existence of a positive solution for nonlinear fractional differential equation, J. math. Anal. appl. 252, 804-812 (2000) · Zbl 0972.34004 · doi:10.1006/jmaa.2000.7123
[9]Zhang, S.: Existence of positive solutions for some class of nonlinear fractional equation, J. math. Anal. appl. 278, 136-148 (2003) · Zbl 1026.34008 · doi:10.1016/S0022-247X(02)00583-8
[10]Jafari, H.; Gejji, V. Daftardar –: Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method, Appl. math. Comput. 180, 700-706 (2006) · Zbl 1102.65136 · doi:10.1016/j.amc.2006.01.007
[11]Xu, X.; Jiang, D.; Yuan, C.: Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear anal. 71, 4676-4688 (2009) · Zbl 1178.34006 · doi:10.1016/j.na.2009.03.030
[12]Zhang, S.: Positive solutions for boundary-value problems of nonlinear fractional equations, Electron. J. Diff. equat. 36, 1-12 (2006) · Zbl 1096.34016 · doi:emis:journals/EJDE/Volumes/2006/36/abstr.html
[13]Qiu, T.; Bai, Z.: Existence of positive solutions for singular fractional equations, Electron. J. Diff. equat. 146, 1-9 (2008) · Zbl 1172.34313 · doi:emis:journals/EJDE/Volumes/2008/146/abstr.html
[14]Bai, Z.; Lü, H.: Positive solutions for boundary value problem of nonlinear fractional equation, J. math. Anal. appl. 311, 495-505 (2005) · Zbl 1079.34048 · doi:10.1016/j.jmaa.2005.02.052
[15]Zhao, Y.; Sun, S.; Han, Z.; Li, Q.: The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations, Commun. nonlinear sci. Numer. simul. 16, 2086-2097 (2011) · Zbl 1221.34068 · doi:10.1016/j.cnsns.2010.08.017
[16]Zhao, Y.; Sun, S.; Han, Z.; Li, Q.: Positive solutions to boundary value problems of nonlinear fractional differential equations, Abstr. appl. Anal. 2011, 1-16 (2011)
[17]Kilbas, A. A.; Srivastava, H. H.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[18]Krasnoselskii, M. A.: Positive solution of operator equation, (1964)