Czasopismo
2013
|
Vol 53, No. 1
|
47--59
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon- Granas type for contractions maps in Fr´echet spaces combined with -resolvent family is the main tool in our analysis.
Czasopismo
Rocznik
Tom
Strony
47--59
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
autor
- Laboratory of mathematics, University of Sidi Bel Abbes PO Box 89, 22000 Sidi Bel Abbes, Algeria , benchohra@univ-sba.dz
autor
- Département de mathématiques et informatique, Universit de Saida 20000, Saida, Algérie
autor
- Département de Mathématiques, Faculté des Sciences, Semlalia B.P.2390, Marrakech, Morocco , ezzinbi@ucam.ac.ma
Bibliografia
- [1] S. Abbas, M. Benchohra and G.M. N’Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012.
- [2] M. Adimy and K. Ezzinbi, The basic theory of abstract semilnear functional differntial equations with nondense domain, in ”Delay Differential Equations with Applications”, ed by O. Arino, M. L. Hbid and E. Ait Dads, NATO Science Series q: Mathematics, Physics and Chemistry, Vol.205, (2006), Springer, Berlin, pp.347-407.
- [3] R. P. Agarwal, M. Belmekki, M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative, Adv. Difference Equ, 9.46 pages.ID 981728.
- [4] E. Ait Dads and K. Ezzinbi, Boundedness and almost periodicity for some state-dependent delay differential equations, Electron. J. Differential Equations. 2002,(67), 13pp.
- [5] W. Arendt, C. Batty, M. Hieber and F. Neubrander, Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, 96, Birkhauser, Basel, 2001.
- [6] S. Baghli, M. Benchohra, J. J. Nieto, Global uniqueness results for partial functional and neutral functional evolution equations with state-dependent delay. J. Advanced Reas. Differ. Equ. 2 (3) (2010), 35-52.
- [7] D. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific, New York, 2012.
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- [9] J. Bélair and M.C. Mackey, Consumer memory and price fluctuations on commodity markets: An integrodifferential model. J. Dynam. Differential Equations 1 (1989), 299-325.
- [10] M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab; Existence results for functional differential equations of fractional order with infinite delay, J. Math. Anal. Appl. 338 (2008), 1340-1350.
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- [12] R.D. Driver, and M.J. Norris, Note on uniqueness for a one-dimensional two- body problem of classical electrodynamics. Ann. Phys. 42 (1967), 347-351.
- [13] K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathemaics,194, Springer-Verlag, New York, 2000.
- [14] M. Frigon and A. Granas, Résultat de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22(1998), 161-168.
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- [16] E. Hernandez, R. Satkhivel and S. Tanaka Aki, Existence results for impulsive evolution differential equations with state-dependent delay, Electron. J. Differential Equations, 2008(28),1-11.
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- [18] Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Unbounded Delay. Springer-Verlag, Berlin, 1991.
- [19] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. ELsevier Science B.V. Amsterdam, 2006.
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- [25] G. M. Mophou and G. M. N’Guérékata, Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay, Appl. Math. Comput. 216(2010), 61-69.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
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