Existence and nonexistence of positive solutions for Dirichlet-type boundary value problem of nonlinear fractional differential equation
-
1844
Downloads
-
3255
Views
Authors
Xinyi Liu
- School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin 130024, P. R. China.
Zhijun Zeng
- School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin 130024, P. R. China.
Abstract
In this paper, we investigate the existence and nonexistence of positive solutions for nonlinear fractional differential equation
boundary value problem. By means of fixed-point theorems on a cone and the properties of Green function, some sufficient
criteria are established. Our results can be considered as an extension of some previous results.
Share and Cite
ISRP Style
Xinyi Liu, Zhijun Zeng, Existence and nonexistence of positive solutions for Dirichlet-type boundary value problem of nonlinear fractional differential equation, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1051--1063
AMA Style
Liu Xinyi, Zeng Zhijun, Existence and nonexistence of positive solutions for Dirichlet-type boundary value problem of nonlinear fractional differential equation. J. Nonlinear Sci. Appl. (2017); 10(3):1051--1063
Chicago/Turabian Style
Liu, Xinyi, Zeng, Zhijun. "Existence and nonexistence of positive solutions for Dirichlet-type boundary value problem of nonlinear fractional differential equation." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1051--1063
Keywords
- Positive solution
- fractional differential equation
- boundary value problem
- the Krasnoselskii fixed point theorem.
MSC
References
-
[1]
M. Al-Akaidi, Fractal speech processing, Cambridge University Press, Cambridge (2004)
-
[2]
A. Babakhani, V. Daftardar-Gejji , Existence of positive solutions of nonlinear fractional differential equations, J. Math. Anal. Appl., 278 (2003), 434–442.
-
[3]
Z. B. Bai, H. S. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311 (2005), 495–505.
-
[4]
L. Bi, M. Bohner, M. Fan, Periodic solutions of functional dynamic equations with infinite delay, Nonlinear Anal., 68 (2008), 1226–1245.
-
[5]
D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204 (1996), 609–625.
-
[6]
D.-Q. Jiang, C.-J. Yuan, The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application, Nonlinear Anal., 72 (2010), 710–719.
-
[7]
M. A. Krasnoselskiı, Positive solutions of operator equations, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron P., Noordhoff Ltd., Groningen (1964)
-
[8]
K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York (1993)
-
[9]
K. B. Oldham, J. Spanier, The fractional calculus, Theory and applications of differentiation and integration to arbitrary order, With an annotated chronological bibliography by Bertram Ross, Mathematics in Science and Engineering, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London (1974)
-
[10]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
-
[11]
D. Ye, M. Fan, H.-Y. Wang, Periodic solutions for scalar functional differential equations, Nonlinear Anal., 62 (2005), 1157–1181.
-
[12]
Z.-J. Zeng, Existence and multiplicity of positive periodic solutions for a class of higher-dimension functional differential equations with impulses, Comput. Math. Appl., 58 (2009), 1911–1920.