zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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 initial and boundary value problems for fractional order mixed type functional differential inclusions. (English) Zbl 1189.34029
Summary: We prove some existence results for initial and boundary value problems for functional differential inclusions of fractional order with both retarded and advanced arguments. The Banach fixed point theorem, the nonlinear alternative of the Leray-Schauder type and the Covitz-Nadler fixed point theorem are the main tools in deriving our proofs.

34A60Differential inclusions
26A33Fractional derivatives and integrals (real functions)
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
45J05Integro-ordinary differential equations
Full Text: DOI
[1] Hilfer, R.: Applications of fractional calculus in physics, (2000) · Zbl 0998.26002
[2] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, North-holland mathematics studies 204 (2006) · Zbl 1092.45003
[3] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and differential equations, (1993) · Zbl 0789.26002
[4] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[5] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives: theory and applications, (1993) · Zbl 0818.26003
[6] El-Sayed, A. M. A.; Gaafar, F. M.: Fractional calculus and some intermediate physical processes, Appl. math. Comput. 144(1), 117-126 (2003) · Zbl 1049.35002 · doi:10.1016/S0096-3003(02)00396-X
[7] Garh, M.; Rao, A.; Kalla, S. L.: Fractional generalization of temperature fields problems in oil strata, Mat. bilten 30, 71-84 (2006) · Zbl 1164.26314
[8] Saxena, R. K.; Kalla, S. L.: On a fractional generalization of free electron laser equation, Appl. math. Comput. 143, 89-97 (2003) · Zbl 1110.45300 · doi:10.1016/S0096-3003(02)00348-X
[9] Saxena, R. K.; Mathai, A. M.; Haubold, H. L.: On generalized fractional kinetic equations, Physica A 344, 657-664 (2004)
[10] Agrawal, O. P.: Analytical schemes for a new class of fractional differential equations, J. phys. A 40, No. 21, 5469-5477 (2007) · Zbl 1126.26007 · doi:10.1088/1751-8113/40/21/001
[11] Lakshmikantham, V.; Devi, J. V.: Theory of fractional differential equations in a Banach space, Eur. J. Pure appl. Math. 1(1), 38-45 (2008) · Zbl 1146.34042 · http://www.ejpam.com/ejpam/index.php/ejpam/article/view/84
[12] Yu, Ch.; Gao, G.: Existence of fractional differential equations, J. math. Anal. appl. 310, 26-29 (2005) · Zbl 1088.34501 · doi:10.1016/j.jmaa.2004.12.015
[13] Kolmanovskii, V.; Myshkis, A.: Introduction to the theory and applications of functional-differential equations, Mathematics and its applications 463 (1999) · Zbl 0917.34001
[14] Hale, J.; Lunel, S. M. Verduyn: Introduction to functional differential equations, Applied mathematical sciences 99 (1993) · Zbl 0787.34002
[15] Darwich, M. A.; Ntouyas, S. K.: Existence results for a fractional functional differential equation of mixed type, Comm. appl. Nonlinear anal. 15, 47-55 (2008) · Zbl 1151.26302
[16] Bai, Z.; Lu, H.: Positive solutions for boundary value problem of nonlinear fractional differential equation, J. math. Anal. appl. 311, 495-505 (2005) · Zbl 1079.34048 · doi:10.1016/j.jmaa.2005.02.052
[17] El-Shahed, M.: Positive solutions for boundary value problem of nonlinear fractional differential equation, Abstr. appl. Anal., 1-8 (2007) · Zbl 1149.26012 · doi:10.1155/2007/10368
[18] Kilbas, A. A.; Trujillo, J. J.: Differential equations of fractional order: methods, results and problems II, Appl. anal. 81, 435-493 (2002) · Zbl 1033.34007 · doi:10.1080/0003681021000022032
[19] Zhang, S.: Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. Differential equations 36, 1-12 (2006) · Zbl 1096.34016 · emis:journals/EJDE/Volumes/2006/36/abstr.html
[20] Deimling, K.: Multivalued differential equations, (1992) · Zbl 0760.34002
[21] Gorniewicz, L.: Topological fixed point theory of multivalued mappings, Mathematics and its applications 495 (1999) · Zbl 0937.55001
[22] Hu, Sh.; Papageorgiou, N.: Theory, Handbook of multivalued analysis (1997) · Zbl 0887.47001
[23] Tolstonogov, A. A.: Differential inclusions in a Banach space, (2000) · Zbl 1021.34002
[24] Granas, A.; Dugundji, J.: Fixed point theory, (2003) · Zbl 1025.47002
[25] Bressan, A.; Colombo, G.: Extensions and selections of maps with decomposable values, Studia math. 90, 69-86 (1988) · Zbl 0677.54013
[26] Covitz, H.; Jr., S. B. Nadler: Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8, 5-11 (1970) · Zbl 0192.59802 · doi:10.1007/BF02771543
[27] Castaing, C.; Valadier, M.: Convex analysis and measurable multifunctions, Lecture notes in mathematics 580 (1977) · Zbl 0346.46038