A global existence and uniqueness result for functional Integro-differential equations in Banach spaces

Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica

Volumn 58, Issue 1, 2012, Pages 56-66

  Benchohra, M ^a   Litimein, S ^a  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

Author keywords

Admissible contractions; Fixed points; Fr chet spaces; Integral resolvent family; Mild solution

Indexed keywords

EID: 84865481288     PISSN: 12218421     EISSN: None     Source Type: Journal    
DOI: 10.2478/v10157-011-0041-0     Document Type: Article

References (23)

1. 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 (2010), 973-1033.
2. Anguraj, A.; Karthikeyan, P.; N'guérékata, G.M. Nonlocal Cauchy problem for some fractional abstract integro-differential equations in Banach spaces, Commun. Math. Anal., 6 (2009), 31-35.
3. Arendt, W.; Batty, C.J.K.; Hieber, M.; Neubrander, F. Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, 96, Birkhäuser Verlag, Basel, 2001.
4. Barbu, V. Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leiden, 1976.
5. Benchohra, M.; Henderson, J.; Ntouyas, S.K.; Ouahab, A. Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338 (2008), 1340-1350.
6. Cuevas, C.; de Souza, J.C. S-asymptotically ω-periodic solutions of semilinear fractional integro-differential equations, Appl. Math. Lett., 22 (2009), 865-870.
7. Cuevas, C.; de Souza, J.C. Existence of S-asymptotically ω-periodic solutions for fractional order functional integro-differential equations with infinite delay, Nonlinear Anal., 72 (2010), 1683-1689.
8. de Andrade, B.; Cuevas, C. S-asymptotically ω-periodic and asymptotically ω-periodic solutions to semi-linear Cauchy problems with non-dense domain, Nonlinear Anal., 72 (2010), 3190-3208.
9. Engel, K.-J.; Nagel, R. One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000.
10. Fattorini, H.O. Second Order Linear Differential Equations in Banach Spaces, North-Holland, Mathematical Studies, 108, North-Holland, Amsterdam, 1985.
11. Frigon, M.; Granas, A. Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec, 22 (1998), 161-168.
12. Hale, J.K.; Kato, J. Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41.
13. Hino, Y.; Murakami, S.; Naito, T. Functional-Differential Equations with Infinite Delay, Lecture Notes in Mathematics, 1473, Springer-Verlag, Berlin, 1991.
14. Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J. Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
15. Lakshmikantham, V.; Leela, S.; Vasundhara, J. Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
16. Lizama, C. Regularized solutions for abstract Volterra equations, J. Math. Anal. Appl., 243 (2000), 278-292.
17. Lizama, C.; S-anchez, J. On perturbation of K-regularized resolvent families, Taiwanese J. Math., 7 (2003), 217-227.
18. N'guérékata, G.M. A Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear Anal., 70 (2009), 1873-1876.
19. Pazy, A. Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.
20. Podlubny, I. Fractional Differential Equations, Mathematics in Science and Engineering, 198, Academic Press, Inc., San Diego, CA, 1999.
21. Prüss, J. Evolutionary Integral Equations and Applications, Monographs in Mathematics, 87, Birkhäuser Verlag, Basel, 1993.
22. Wang, R.N.; Chen, D.H. On a class of retarded integro-differential equations with nonlocal initial conditions, Comput. Math. Appl., 59 (2010), 3700-3709.
23. Yosida, K. Functional Analysis, Sixth edition, 123, Springer-Verlag, Berlin-New York, 1980.