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)
Positive solutions for system of nonlinear fractional differential equations in two dimensions with delay. (English) Zbl 1197.34155
Summary: We investigate the existence and uniqueness of positive solutions for a system of nonlinear fractional differential equations in two dimensions with delay. Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem in a cone.

34K37Functional-differential equations with fractional derivatives
47N20Applications of operator theory to differential and integral equations
Full Text: DOI EuDML
[1] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Application, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. · Zbl 0924.34008
[2] K. B. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiely, New York, NY, USA, 1993. · Zbl 0789.26002
[3] K. B. Oldham and I. Spanier, The Fractional Calculus, Academic Press, Londan, UK, 1997. · Zbl 0428.26004
[4] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science, Yverdon, Switzerland, 1993. · Zbl 0818.26003
[5] B. J. West, M. Bologna, and P. Grigolini, Eds., Physics of Fractal Operators, Springer, New York, NY, USA, 2003.
[6] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993. · Zbl 0787.34002
[7] J. Ander and P. Seibert, “Ü ber die stückweise linearen differentiallgleichungen, die bei regelungsproblemen auftreten,” Archiv der Mathematik, vol. 7, no. 3, pp. 148-164, 1956. · Zbl 0071.34302 · doi:10.1007/BF01899571
[8] S. V. Drakunov and V. I. Utkin, “Sliding mode control in dynamic systems,” International Journal of Control, vol. 55, no. 4, pp. 1029-1037, 1992. · Zbl 0745.93031 · doi:10.1080/00207179208934270
[9] E. Shustin, “Dynamics of oscillations in a multi-dimensional delay differential system,” Discrete and Continuous Dynamical Systems. Series A, vol. 11, no. 2-3, pp. 557-576, 2004. · Zbl 1063.34065 · doi:10.3934/dcds.2004.11.557
[10] S. Roy, A. Saberi, and Y. Wan, “On multiple-delay output feedback stabilization of LTI plants,” International Journal of Robust and Nonlinear Control. In press. · Zbl 1200.93115
[11] A. Oustaloup, Systèms Asservis Lineaires d’Ordre Fractionnaire, Masson, Paris, France, 1983.
[12] A. Oustaloup, La Command CRONE, série Automatique, Hermès, Paris, France, 1991.
[13] V. Daftardar-Gejji and A. Babakhani, “Analysis of a system of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 511-522, 2004. · Zbl 1058.34002 · doi:10.1016/j.jmaa.2004.01.013
[14] V. Daftardar-Gejji and H. Jafari, “Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives,” Journal of Mathematical Analysis and Applications, vol. 328, no. 2, pp. 1026-1033, 2007. · Zbl 1115.34006 · doi:10.1016/j.jmaa.2006.06.007
[15] M. C. Joshi and R. K. Bose, Some Topics in Nonlinear Functional Analysis, A Halsted Press Book, Wiley Eastern Limited, New Dehli, India, 1985. · Zbl 0596.47038
[16] M. A. Krasnoselskiĭ, Positive Solutions of Operator Equations, P. Noordhoff, Groningen, The Netherlands, 1964.
[17] A. Babakhani and V. Daftardar-Gejji, “Existence of positive solutions of nonlinear fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 278, no. 2, pp. 434-442, 2003. · Zbl 1027.34003 · doi:10.1016/S0022-247X(02)00716-3
[18] C.-Z. Bai and J.-X. Fang, “The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 150, no. 3, pp. 611-621, 2004. · Zbl 1061.34001 · doi:10.1016/S0096-3003(03)00294-7