Optimal mild solutions and weighted pseudo-almost periodic classical solutions of fractional integro-differential equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 74, Issue 1, 2011, Pages 224-234

  Cao, Junfei ^a   Yang, Qigui ^a   Huang, Zaitang ^a,b  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b Wuzhou University   (China)

Author keywords

Existence and uniqueness; Fractional integro differential equations; Optimal mild solutions; Weighted pseudo almost periodic classical solutions

Indexed keywords

ALMOST PERIODIC; CLASSICAL SOLUTIONS; EXISTENCE AND UNIQUENESS; FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION; MILD SOLUTION;

INTEGRODIFFERENTIAL EQUATIONS;

OPTIMIZATION;

EID: 77957674255     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2010.08.036     Document Type: Article

References (42)

1. C. Zhang Pseudo almost periodic solutions of some differential equations J. Math. Anal. Appl. 151 1994 62 76
2. C. Zhang Integration of vector-valued pseudo almost periodic functions Proc. Amer. Math. Soc. 121 1994 167 174
3. C. Zhang Pseudo almost periodic solutions of some differential equations II J. Math. Anal. Appl. 192 1995 543 561
4. E. Dads, K. Ezzinbi, and O. Arino Pseudo-almost periodic solutions for some differential equations in a Banach space Nonlinear Anal. TMA 28 1997 1141 1155
5. C. Cuevas, and M. Pinto Existence and uniqueness of pseudo almost periodic solutions of semilinar Cauchy problems with non dense domain Nonlinear Anal. TMA 45 2001 73 83
6. T. Diagana Pseudo Almost Periodic Functions in Banach Spaces 2007 Nova Science Publishers, Inc. New York
7. C. Cuevas, and H. Herndez Pseudo almost periodic solutions for abstract partial functional differential equations Appl. Math. Lett. 22 2009 534 538
8. T. Diagana Weighted pseudo almost periodic functions and applications C. R. Acad. Sci. Paris, Ser. I 343 2006 643 646
9. V. Ahn, and R. McVinisch Fractional differential equations driven by Lvy noise J. Appl. Math. Stoch. Anal. 16 2003 97 119
10. D. Benson, The fractional advectiondispersion equation, Ph.D. Thesis, University of Nevada, Reno, NV, 1998.
11. R. Schumer, and D. Benson Eulerian derivative of the fractional advectiondispersion equation J. Contam. Hydrol. 48 2001 69 88
12. M. Borai Some probability densities and fundamental solutions of fractional evolutions equations Chaos Solitons Fractals 14 2002 433 440
13. A. Sayed Nonlinear functionaldifferential equations of arbitrary orders Nonlinear Anal. TMA 33 1998 181 186
14. G. Mophou, and G. N'Gurkata Existence of mild solution for some fractional differential equations with nonlocal conditions Semigroup Forum 79 2009 315 322
15. G. N'Gurkata Cauchy problem for some fractional abstract differential equation with nonlocal conditions Nonlinear Anal. TMA 70 2009 1873 1876
16. V. Lahshmikantham, and J. Devi Theory of fractional differential equations in Banach spaces Eur. J. Pure Appl. Math. 1 2008 38 45
17. W. Glockle, and T. Nonnemacher A fractional calculus approach of self-similar protein dynamics Biophys. J. 68 1995 46 53
18. F. Metzler, W. Schick, H. Kilian, and T. Nonnemacher Relaxation in filled polymers: a fractional calculus approach J. Chem. Phys. 103 1995 7180 7186
19. B. Ahmad, and S. Sivasundaram Some existence results for fractional integrodifferential equations with nonlinear conditions Commun. Math. Anal. 12 2008 107 112
20. T. Bhaskar, V. Lakshmikantham, and S. Leela Fractional differential equations with KrasnoselskiiKrein-type condition Nonlinear Anal. Hybrid Syst. 3 2009 734 737
21. V. Lakshmikantham, and S. Leela Nagumo-type uniqueness result for fractional differential equations Nonlinear Anal. TMA 71 2009 2886 2889
22. A. Anguraj, P. Karthikeyan, and G. N'Gurkata Nonlocal Cauchy problem for some fractional abstract integrodifferential equations in Banach spaces Commun. Math. Anal. 6 2009 31 35
23. D. Bahuguna, and S. Srvastavai Semilinear integrodifferential equations with compact semigroup J. Appl. Math. Stoch. Anal. 11 1998 507 517
24. J. Dieudonne Foundation of Modern Analysis 1960 Academic Press New York
25. J. Yorke A continuous differential equation in Hilbert space without existence Funkcial. Ekvac. 12 1970 19 21
26. M. Rashid, and Y. El-Qaderi Semilinear fractional integrodifferential equations with compact semigroup Nonlinear Anal. TMA 71 2009 6276 6282
27. K. Balachandran, and J. Park Nonlocal Cauchy problem for abstract fractional semilinear evolution equations Nonlinear Anal. TMA 71 2009 4471 4475
28. G. Mophou, and G. N'Gurkata Mild solutions for semilinear fractional differential equations Electron. J. Differential Equations 21 2009 1 9
29. Y. Changa, V. Kavitha, and M. Arjunan Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order Nonlinear Anal. TMA 71 2009 5551 5559
30. M. Heard, and S. Rankin A semilinear parabolic integrodifferential equation J. Differential Equations 71 1988 201 233
31. G. Mophou, and G. N'Gurkata A note on a semilinear fractional differential equation of a neutral type with infinite delay Adv. Difference Equ. 2010 2010 Article ID 674630, 8 pages
32. F. Li, and G. N'Gurkata Existence and uniqueness of mild solution for fractional integrodifferential equations Adv. Difference Equ. 2010 2010 Article ID 158789, 10 pages
33. I. Podlubny, Fractional Differential Equations, Math. in Science and Eng., Technical University of Kosice, Slovak Republic, 1999.
34. A. Pazy Semigroups of Linear Operators and Applications to Partial Differential Equations 1983 Springer-Verlag New York
35. T. Diagana Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations J. Math. Anal. Appl. 350 2009 18 28
36. R. Agarwal, T. Diagana, and E. Hernndez Weighted pseudo almost periodic solutions to some partial neutral functional differential equations J. Nonlinear Convex Anal. 8 2007 397 415
37. T. Diagana Weighted pseudo almost periodic solutions to some differential equations Nonlinear Anal. TMA 68 2008 2250 2260
38. W. Feller An Introduction to Probability Theory and its Applications vol. II 1971 Wiley New York
39. G. N'Gurkata Almost Automorphic and Almost Periodic Functions in Abstract Spaces 2001 Kluwer Academic, Plenum Publishers New York
40. R. Larsen Functional Analysis 1973 Decker Inc. New York
41. T. Yoshizawa Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions 1975 Springer-Verlag New York
42. S. Zaidman Abstract Differential Equations 1979 Pitman Publishing San Francisco, London, Melbourne