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)
A singular boundary value problem for nonlinear differential equations of fractional order. (English) Zbl 1191.34006
The paper studies a Dirichlet boundary value problem for equations of fractional order based on the Riemann Liouville fractional derivative. The authors obtain existence results by using the Leray-Schauder continuation principle and use Hölder’s inequality to obtain a priori estimates. The authors also indicate how their methods in this paper may improve the results of other recent papers.
MSC:
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
References:
[1]Bai, C.Z., Fang, J.X.: The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations. Appl. Math. Comput. 150, 611–621 (2004) · Zbl 1061.34001 · doi:10.1016/S0096-3003(03)00294-7
[2]Bai, Z., Lü, 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
[3]Benchohra, M., Henderson, J., Ntoyuas, S.K., Quahab, A.: Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338, 1340–1350 (2008) · Zbl 1209.34096 · doi:10.1016/j.jmaa.2007.06.021
[4]Daftardar-Gejji, V.: 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
[5]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
[6]Diethelm, K., Freed, A.D.: On the solution of nolinear fractional order differential equations used in the modelling of viscoplasticity. In: Keil, F., Mackens, W., Voss, H. (eds.) Scientific Computing in Chemical Engineering II–Computational Fluid Dynamics and Molecular Properties, pp. 217–224. Springer, Heidelberg (1999)
[7]El-Sayed, W.G., El-Sayed, A.M.A.: On the functional integral equations of mixed type and integro-differential equations of fractional orders. Appl. Math. Comput. 154, 461–467 (2004) · Zbl 1061.45004 · doi:10.1016/S0096-3003(03)00727-6
[8]García-Huidobro, M., Gupta, C.P., Manásevich, R.: A Dirichlet-Neumann m-point BVP with a p-Laplacian-like operator. Nonlinear Anal. 62(6), 1067–1089 (2005) · Zbl 1082.34011 · doi:10.1016/j.na.2005.04.020
[9]Gupta, C.P.: A non-resonant multi-point boundary value problem of Neumann-Dirichlet type for a p-Laplacian type operator. Dyn. Syst. Appl. 4, 439–442 (2004)
[10]Gupta, C.P., Trofimchuk, S.: A priori estimates for the existence of a solution for a multi-point boundary value problem. J. Inequal. Appl. 5(4), 351–365 (2000) · Zbl 0967.34006 · doi:10.1155/S1025583400000187
[11]Jaradat, O.K., Al-Omari, A., Momani, S.: Existence of the mild solution for fractional semilinear initial value problems. Nonlinear Anal. (2007). doi: 10.1016/j.na.2007.09.008
[12]Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)
[13]Kiryakova, V.S.: Generalized Fractional Calculus and Applications. Chapman & Hall, London (1993)
[14]Krasnosel’skiĭ, M.A.: Topological Methods in the Theory of Nonlinear Integral Equations (trans: Armstrong, A.H.). Pergamon, Elmsford (1964)
[15]Lakshmikantham, V.: Theory of fractional functional differential equations. Nonlinear Anal. (2007). doi: 10.1016/j.na.2007.09.025
[16]Lakshmikantham, V., Vatsala, A.S.: Basic theory of fractional differential equations. Nonlinear Anal. (2007). doi: 10.1016/j.na/207.08.042
[17]Leggett, R.W., Williams, L.R.: Multiple positive fixed points of operators on ordered Banach spaces. Indiana Univ. Math. J. 28, 673–688 (1979) · Zbl 0421.47033 · doi:10.1512/iumj.1979.28.28046
[18]Li, C., Deng, W.: Remarks on fractional derivatives. Appl. Math. Comput. 187, 777–784 (2007) · Zbl 1125.26009 · doi:10.1016/j.amc.2006.08.163
[19]Ma, R., O’Regan, D.: Solvability of singular second order m-point boundary value problems. J. Math. Anal. Appl. 301, 124–134 (2005) · Zbl 1062.34018 · doi:10.1016/j.jmaa.2004.07.009
[20]Podlubny, I.: Fractional Differential Equations. Mathematics in Sciences and Applications, vol. 198. Academic Press, San Diego (1999)
[21]Sabatier, J., Agrawal, O.P., Tenreiro-Machado, J.A.: Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, New York (2007)
[22]Samko, S.G., Kilbas, A.A., Mirichev, O.I.: Fractional Integral and Derivatives (Theory and Applications). Gordon and Breach, New York (1993)
[23]Zeidler, E.: Nonlinear Functional Analysis and Applications, I: Fixed Point Theorems. Springer, New York (1986)