Solvability of a two-point fractional boundary value problem
-
1888
Downloads
-
3411
Views
Authors
Assia Guezane-Lakoud
- Laboratory of Advanced Materials, Faculty of Sciences, Badji Mokhtar-Annaba University, P. O. Box 12, 23000 Annaba, Algeria.
Rabah Khaldi
- Laboratory LASEA. Faculty of Sciences, Badji Mokhtar-Annaba University, P. O. Box 12, 23000 Annaba, Algeria.
Abstract
The aim of this paper is the study of the existence and uniqueness of solutions for a two-point fractional
boundary value problem, by means of Banach contraction principle and Leray Schauder nonlinear alternative.
Some examples are given.
Share and Cite
ISRP Style
Assia Guezane-Lakoud, Rabah Khaldi, Solvability of a two-point fractional boundary value problem, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 1, 64--73
AMA Style
Guezane-Lakoud Assia, Khaldi Rabah, Solvability of a two-point fractional boundary value problem. J. Nonlinear Sci. Appl. (2012); 5(1):64--73
Chicago/Turabian Style
Guezane-Lakoud, Assia, Khaldi, Rabah. "Solvability of a two-point fractional boundary value problem." Journal of Nonlinear Sciences and Applications, 5, no. 1 (2012): 64--73
Keywords
- Fractional Caputo derivative
- Banach Contraction principle
- Leray Schauder nonlinear alternative.
MSC
References
-
[1]
G. A. Anastassiou, On right fractional calculus , Chaos, Solitons and Fractals, 42 (2009), 365-376.
-
[2]
C. Z. Bai , Triple positive solutions for a boundary value problem of nonlinear fractional differential equation, Electron. J. Qual. Theory Diff. Equ. , 24 (2008), 1-10.
-
[3]
R. L. Bagley, A theoretical basis for the application of fractional calculus to viscoelasticity, Journal of Rheology, 27 (3) (1983), 201-210.
-
[4]
K. Deimling, Nonlinear functional analysis, Springer, Berlin (1985)
-
[5]
R. Hilfer, Application of Fractional Calculus in Physics, World Scientific Singapur, (2000), 699-707.
-
[6]
H. Jafari, V. Daftardar-Gejji, Positive solutions of nonlinear fractional boundary value problems using adomian decomposition method , Appl. Math. Comput. , 180 (2006), 700-706.
-
[7]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, in: Jan van Mill (Ed.), Theory and Applications of Fractional Differential Equations, in: North-Holland Mathematics Studies, 204, Elsevier, Amsterdam, The Netherlands (2006)
-
[8]
S. Liang, J. Zhang, Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fractional differential equation, J Appl Math Comput, DOI 10.1007/s12190-011-0475-2. ()
-
[9]
S. Liang , J. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equation, Nonlinear Analysis, 71 (2009), 5545- 5550.
-
[10]
K. B. Oldham, Fractional differential equations in electrochemistry, Advances in Engineering Software, (2009)
-
[11]
I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 1998, Academic Press, New York, London, Toronto (1999)
-
[12]
T. Qiu, Z. Bai , Existence of positive solutions for singular fractional equations, Electron. J. Diff. Equat. , 146 (2008), 1-9.
-
[13]
X. Su, L. Liu, Existence of solution for boundary value problem of nonlinear fractional differential equation, Appl. Math. J. Chinese Univ. Ser. B, 22 (3) (2007), 291-298.
-
[14]
X. Xu, D. Jiang, C. Yuan, Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear Anal, 71 (2009), 4676-4688.
-
[15]
Y. Zhao, S. Sun, Z. Han, M. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Applied Mathematics and Computation, 217 (2011), 6950-6958.
-
[16]
Y. Zhao, S. Sun, Z. Han, Q. Li, The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations, Commun. Nonlinear Sci. Numer. Simul. , 16 (2011), 2086-2097.