Asymptotically almost automorphic solutions of abstract fractional integro-differential neutral equations

Applied Mathematics Letters

Volumn 23, Issue 9, 2010, Pages 960-965

  dos Santos, José Paulo Carvalho ^a   Cuevas, Claudio ^b  

^a FEDERAL UNIVERSITY OF ALFENAS   (Brazil)

^b FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

Asymptotically almost automorphic function; Compact asymptotically almost automorphic functions; Fractional integro differential neutral equations; Phase space

Indexed keywords

ALMOST AUTOMORPHIC; ALMOST AUTOMORPHIC FUNCTION; NEUTRAL EQUATIONS; PHASE SPACES;

ABSTRACTING; PHASE SPACE METHODS;

ASYMPTOTIC ANALYSIS;

EID: 77953685565     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2010.04.016     Document Type: Article

References (31)

1. Cuesta E. Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations. Discrete Contin. Dyn. Syst. Suppl. (2007) 277-285
2. Cuesta E., and Palencia C. A numerical method for an integro-differential equation with memory in Banach spaces: qualitative properties. SIAM J. Numer. Anal. 41 (2003) 1232-1241
3. Cuevas C., and de Souza J. S-asymptotically ω-periodic solutions of semilinear fractional integro-differential equations. Appl. Math. Lett. 22 (2009) 865-870
4. Hale J.K., and Verduyn Lunel S.M. Introduction to Functional-Differential Equations. Applied Mathematical Sciences vol. 99 (1993), Springer-Verlag, New York
5. Henríquez H.R., Hernández E., and dos Santos J.P.C. Asymptotically almost periodic and almost periodic solutions for partial neutral integrodifferential equations. Z. Anal. Anwend. 26 3 (2007) 261-375
6. Hernández E., and Henríquez H.R. Existence results for partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl. 221 2 (1998) 452-475
7. Hernández E., and Henríquez H.R. Existence of periodic solutions of partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl. 221 1 (1998) 499-522
8. Hernández E., and dos Santos J.P.C. Existence results for partial neutral integro differential equations with unbounded delay. Appl. Anal. 86 2 (2007) 223-237
9. Wu J. Theory and Applications of Partial Functional-Differential Equations. Applied Mathematical Sciences vol. 119 (1996), Springer-Verlag, New York
10. Ahn V.V., and McVinish R. Fractional differential equations driven by Levy noise. J. Appl. Stoch. Anal. 16 2 (2003) 97-119
11. Eidelman S.D., and Kochubei A.N. Cauchy problem for fractional diffusion equations. J. Differential Equations 199 (2004) 211-255
12. Gorenflo R., and Mainardi F. Fractional calculus: integral and differential equations of fractional order. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer-Verlag, Vienna, New York 223-276
13. Agarwal R.P., de Andrade B., and Cuevas C. On type of periodicity and ergodicity to a class of fractional order differential equations. Adv. Differential Equ. 2010 (2010) 1-25 Article ID 179750
14. R.P. Agarwal, B. de Andrade, C. Cuevas, Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations, Nonlinear Anal. RWA. doi:10.1016/j.nonrwa.2010.01.002.
15. Cuevas C., and de Souza J. Existence of S-asymptotically ω-periodic solutions for fractional order integro-differential equations with infinite delay. Nonlinear Anal. (2009) 10.1016/j.na.2009.09.007
16. Cuevas C., and Lizama C. Almost automorphic solutions to a class of semilinear fractional differential equations. Appl. Math. Lett. 21 (2008) 1315-1319
17. Cuevas C., Rabelo M., and Soto H. Pseudo almost automorphic solutions to a class of semilinear fractional differential equations. Commun. Appl. Nonlinear Anal. 17 (2010) 33-48
18. Agarwal R.P., Diagana T., and Hernández E. Weighted pseudo almost periodic solutions to some partial neutral functional differential equations. J. Nonlinear Convex Anal. 8 3 (2007) 397-415
19. de Andrade B., and Cuevas C. Almost automorphic and pseudo almost automorphic solutions to semilinear evolutions equations with non dense domain. J. Inequal. Appl. 2009 (2009) 1-9 10.1155/2009/298207 Article ID 2982207
20. Bochner S. A new approach to almost periodicity. Proc. Natl. Acad. Sci. USA 48 (1962) 2039-2043
21. Cuevas C., and Hernández H. Pseudo-almost periodic solutions for abstract partial functional differential equations. Appl. Math. Lett. 22 (2009) 534-538
22. Cuevas C., and Pinto M. Existence and uniqueness of pseudo-almost periodic solutions of semilinear Cauchy problems with nondense domain. Nonlinear Anal. 45 1 (2001) 73-83
23. Diagana T., Henríquez H.R., and Hernández E. Almost automorphic mild solutions to some partial neutral functional-differential equations and applications. Nonlinear Anal. 69 5-6 (2008) 1485-1493
24. Diagana T., and N'Guérékata G.M. Almost automorphic solutions to some classes of partial evolution equations. Appl. Math. Lett. 20 4 (2007) 462-466
25. Diagana T., N'Guérékata G.M., and Minh N.V. Almost automorphic solutions of evolution equations. Proc. Amer. Math. Soc. 132 11 (2004) 3289-3298
26. Ding H.S., Xiao T., and Liang J. Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions. J. Math. Anal. Appl. 338 1 (2008) 141-151
27. N'Guérékata G.M. Topics in Almost Automorphy (2005), Springer, New York, Boston, Dordrecht, London, Moscow
28. N'Guérékata G.M. Sur les solutions presque automorphes d'équations différentielles abstraites. Ann. Sci. Math. Québec. 1 (1981) 69-79
29. Bugajewski D., and N'Guérékata G.M. On the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces. Nonlinear Anal. 59 8 (2004) 1333-1345
30. Diagana T., Hernández E., and Dos Santos J.P.C. Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations. Nonlinear Anal. 71 (2009) 248-257
31. Hino Y., Murakami S., and Naito T. Functional-Differential Equations with Infinite Delay. Lecture Notes in Mathematics vol. 1473 (1991), Springer-Verlag, Berlin