Abstract
In this paper, we study the existence of positive solution to boundary value problem for fractional differential system
where \({D_{0^+}^\alpha}\) is the Riemann-Liouville fractional derivative of order α. By using the Leggett-Williams fixed point theorem in a cone, the existence of three positive solutions for nonlinear singular boundary value problems is obtained.
Article PDF
Similar content being viewed by others
References
El-Sayed A.M.A.: Nonlinear functional differential equations of arbitrary orders. Nonlinear Anal. 33, 181–186 (1998)
Kilbas A.A., Trujillo J.J.: Differential equations of fractional order: Methods, results and problems I. Appl. Anal. 78, 153–192 (2001)
Kilbas A.A., Trujillo J.J.: Differential equations of fractional order: Methods, results and problems II. Appl. Anal. 81, 435–493 (2002)
Agarwal R.P., Benchohra M., Hamani S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109, 973–1033 (2010)
Lakshmikantham V., Leela S., Devi J.V.: Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, Cambridge (2009)
Lakshmikantham V., Vatsala A.S.: Basic theory of fractional differential equations. Nonlinear Anal. TMA 69(8), 2677–2682 (2008)
Podlubny I.: Fractional Differential Equations. Academic Press, New York (1999)
Samko G., Kilbas A., Marichev O.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Amsterdam (1993)
Saadi A., Benbachir M.: Positive solutions for three-point nonlinear fractional boundary value problems. Electron. J. Qual. Theory Differ. Equ. 2, 1–19 (2011)
Kilbas A.A., Srivastava H.M., Trujillo J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
Leggett R.W., Williams L.R.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana Univ. Math. J. 28, 673–688 (1979)
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
N. Nyamoradi thanks Razi University for support.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Nyamoradi, N. Multiple positive solutions for fractional differential systems. Ann Univ Ferrara 58, 359–369 (2012). https://doi.org/10.1007/s11565-012-0155-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11565-012-0155-7