1 |
S. Abbas and M. Benchohra, Upper and lower solutions method for darboux problem for fractional order implicit impulsive partial hyperbolic differential equations, Acta Univ. Palacki. Olomuc. Fac. Rer. Nat. Mathematica 51 (2012), no. 2, 5-18.
|
2 |
R. P. Agarwal, M. Benchohra, and B. A. Slimani, Existence results for differential equations with fractional order and impulses, Mem. Differential Equations Math. Phys. 44 (2008), 1-21.
DOI
ScienceOn
|
3 |
B. Ahmad and S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Anal. Hybrid Syst. 3 (2009), no. 3, 251-258.
DOI
ScienceOn
|
4 |
B. Ahmad, Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear Anal. Hybrid Syst. 4 (2010), no. 1, 134-141.
DOI
ScienceOn
|
5 |
K. Balachandran and S. Kiruthika, Existence of solutions of abstract fractional impulsive semilinear evolution equations, Electron. J. Qual. Theory Differ. Equ. 4 (2010), no. 4, 12 pp.
|
6 |
J. Bana's and K. Goebel, Measure of Noncompactness in Banach Spaces, Marcel Dekker Inc., New York, 1980.
|
7 |
E. Bazhlekova, Fractional evolution equations in Banach spaces, Ph.D. Thesis, Eindhoven University of Technology, 2001.
|
8 |
R. Bellman, The stability of solutions of linear differential equations, Duke Math. J. 10 (1943), no. 4, 643-647.
DOI
|
9 |
M. Belmekki and M. Benchohra, Existence result for fractional order semilinear functional differential equations with nondense domain, Nonlinear Anal. 72 (2010), no. 2, 925-932.
DOI
ScienceOn
|
10 |
M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, Existence results for fractional functional differential inclusions with infinite delay and application to control theory, Fract. Calc. Appl. Anal. 11 (2008), no. 1, 35-56.
|
11 |
M. Benchohra and B. A. Slimani, Existence and uniqueness of solutions to impulsive fractional differential equations, Electron. J. Differential Equations 2009 (2009), no. 10, 11 pp.
|
12 |
P. Benilan, Equations d'evolution dans un espace de Banach quelconque et applications, Th'ese de doctorat d'etat, Orsay, 1972.
|
13 |
D. Bothe, Multivalued perturbation of m-accretive differential inclusions, lsrael. J. Math. 108 (1998), 109-138.
|
14 |
D. J. Guo, V. Lakshmikantham, and X. Z. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic, Dordrecht, 1996.
|
15 |
K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.
|
16 |
Z. Denton, P. W. Ng, and A. S. Vatsala, Quasilinearization method via lower and upper solutions for Riemann-Liouville fractional differential equations, Nonlinear Dyn. Syst. Theory 11 (2011), no. 3, 239-251.
|
17 |
H. Fan and J. Mu, Initial value problem for fractional evolution equations, Adv. Difference Equ. 2012 (2012), no. 49, 10 pp.; doi:10.1186/1687-1847-2012-49.
DOI
ScienceOn
|
18 |
H.-P. Heinz, On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions, Nonlinear Anal 7 (1983), no. 12, 1351-1371.
DOI
ScienceOn
|
19 |
L. Hu, Y. Ren, and R. Sakthivel, Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays, Semigroup Forum 79 (2009), no. 3, 507-514.
|
20 |
R. W. Ibrahim and S. Momani, Upper and lower bounds of solutions for fractional integral equations, Surv. Math. Appl. 2 (2007), 145-156.
|
21 |
O. K. Jaradat, A. Al-Omari, and S. Momani, Existence of the mild solution for fractional semilinear initial value problems, Nonlinear Anal. 69 (2008), no. 9, 3153-3159.
DOI
ScienceOn
|
22 |
V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, New York, 1969.
|
23 |
L. Lin, X. Liu, and H. Fang, Method of upper and lower solutions for fractional differential equations, Electron. J. Differential Equations 2012 (2012), no. 100, 13 pp.
|
24 |
J. Mu, Monotone iterative technique for fractional evolution equations in Banach spaces, J. Appl. Math. 2011 (2011), Art. ID 767186, 13 pp.
|
25 |
F. Mainardi, P. Paradisi, and R. Gorenflo, Probability distributions generated by fractional diffusion equations, J. Kertesz, I. Kondor (Eds.), Econophysics: An Emerging Science, Kluwer, Dordrecht, 2000.
|
26 |
H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), no. 5, 985-999.
DOI
ScienceOn
|
27 |
G. M. Mophou, Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear Anal. 72 (2010), no. 304, 1604-1615.
DOI
ScienceOn
|
28 |
I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
|
29 |
X. Shu, Y. Lai, and Y. Chen, The existence of mild solutions for impulsive fractional partial differential equations, Nonlinear Anal. 74 (2011), no. 5, 2003-2011.
DOI
ScienceOn
|
30 |
X. Shu and Q. Wang, The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1 < < 2, Comput. Math. Appl. 64 (2012), no. 6, 2100-2110.
DOI
ScienceOn
|
31 |
Z. Tai and X. Wang, Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces, Appl. Math. Lett. 22 (2009), no. 11, 1760-1765.
DOI
ScienceOn
|
32 |
C. Wang, H. Yuan, and S. Wang, On positive solution of nonlinear fractional differential equation, World Appl. Sci. J. 18 (2012), no. 11, 1540-1545.
|
33 |
S. Zhang and X. Su, Existence of extreme solutions for fractional order boundary value problem using upper and lower solutions method in reverst order, J. Fract. Calc. Appl. 2 (2012), no. 6, 1-14.
|
34 |
A. Yakar, Initial time difference quasilinearization for Caputo fractional differential equations, Adv. Difference Equ. 2012 (2012), no. 92, 9 pp.
DOI
ScienceOn
|