Monotone iterative technique for fractional evolution equations in banach spaces

Journal of Applied Mathematics

Volumn 2011, Issue , 2011, Pages

  Mu, Jia ^a  

^a NORTHWEST NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 81755161262     PISSN: 1110757X     EISSN: 16870042     Source Type: Journal    
DOI: 10.1155/2011/767186     Document Type: Article

References (56)

1. Chen G., Friedman G., An RLC interconnect model based on Fourier analysis IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems 2005 24 2 170 183
2. Lundstrom B., Higgs M., Spain W., Fairhall A., Fractional differentiation by neocortical pyramidal neurons Nature Neuroscience 2008 11 11 1335 1342
3. Rossikhin Y., Shitikova M., Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems Acta Mechanica 1997 120 14 109 125 (Pubitemid 127544483)
4. Westerlund S., Ekstam L., Capacitor theory IEEE Transactions on Dielectrics and Electrical Insulation 1994 1 5 826 839
5. Li Z. B., An extended fractional complex transform International Journal of Nonlinear Sciences and Numerical Simulation 2010 11 335 338
6. Li Z. B., He J. H., Fractional complex transform for fractional differential equations Mathematical and Computational Applications 2010 15 5 970 973
7. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 Amsterdam, The Netherlands Elsevier
8. Hilfer R., Applications of Fractional Calculus in Physics 2000 Singapore World Scientific
9. Balachandran K., Kiruthika S., Trujillo J. J., Existence results for fractional impulsive integrodifferential equations in Banach spaces Communications in Nonlinear Science and Numerical Simulation 2011 16 4 1970 1977
10. Balachandran K., Park J. Y., Nonlocal Cauchy problem for abstract fractional semilinear evolution equations Nonlinear Analysis 2009 71 10 4471 4475
11. Bazhlekova E., Fractional Evolution Equations in Banach Spaces, Ph.D. thesis 2001 Eindhoven, The Netherlands Eindhoven University of Technology
12. El-Borai M. M., Some probability densities and fundamental solutions of fractional evolution equations Chaos, Solitons and Fractals 2002 14 3 433 440 (Pubitemid 34182465)
13. El-Borai M. M., The fundamental solutions for fractional evolution equations of parabolic type Journal of Applied Mathematics and Stochastic Analysis 2004 3 197 211
14. Hernndez E., Oregan D., Balachandran K., On recent developments in the theory of abstract differential equations with fractional derivatives Nonlinear Analysis 2010 73 10 3462 3471
15. Kaikina E. I., Nonlinear evolution equations with a fractional derivative on a half-line Nonlinear Analysis 2009 71 3-4 766 781
16. Odibat Z. M., Compact and noncompact structures for nonlinear fractional evolution equations Physics Letters A 2008 372 8 1219 1227
17. Shu X.-B., The existence of mild solutions for impulsive fractional partial differential equations Nonlinear Analysis 2011 74 5 2003 2011
18. Wang J., Zhou Y., Wei W., A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces Communications in Nonlinear Science and Numerical Simulation 2011 16 10 4049 4059
19. Wang J., Zhou Y., A class of fractional evolution equations and optimal controls Nonlinear Analysis 2011 12 1 262 272
20. Wang J., Zhou Y., Wei W., Xu H., Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls Computers and Mathematics with Applications 2011 62 3 1427 1441
21. Wang R.-N., A note on the fractional Cauchy problems with nonlocal initial conditions Applied Mathematics Letters 2011 24 8 1435 1442
22. Zhou Y., Jiao F., Existence of mild solutions for fractional neutral evolution equations Computers and Mathematics with Applications 2010 59 3 1063 1077
23. Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations Nonlinear Analysis 2010 11 5 4465 4475
24. Baeumer B., Kurita S., Meerschaert M. M., Inhomogeneous fractional diffusion equations Fractional Calculus and Applied Analysis 2005 8 4 375 397
25. Henderson J., Ouahab A., Fractional functional differential inclusions with finite delay Nonlinear Analysis 2009 70 5 2091 2105
26. Meerschaert M. M., Benson D. A., Scheffler H., Baeumer B., Stochastic solution of space-time fractional diffusion equations Physical Review E 2002 65 4 1103 1106
27. Du S., Lakshmikantham V., Monotone iterative technique for differential equations in a Banach space Journal of Mathematical Analysis and Applications 1982 87 2 454 459
28. Li Y., Existence and uniqueness of positive periodic solutions for abstract semilinear evolution equations Journal of Systems Science and Mathematical Sciences 2005 25 6 720 728
29. Li Y., Existence of solutions to initial value problems for abstract semilinear evolution equations Acta Mathematica Sinica 2005 48 6 1089 1094 (Pubitemid 43153568)
30. Li Y., Periodic solutions of semilinear evolution equations in Banach spaces Acta Mathematica Sinica 1998 41 3 629 636 (Pubitemid 128083244)
31. Li Y., The global solutions of inition value problems for abstract semilinear evolution equations Acta Analysis Functionalis Applicata 2001 3 4 339 347
32. Li Y., The positive solutions of abstract semilinear evolution equations and their applications Acta Mathematica Sinica 1996 39 5 666 672 (Pubitemid 126137947)
33. Yang H., Monotone iterative technique for the initial value problems of impulsive evolution equations in ordered Banach spaces Abstract and Applied Analysis 2010 2010 11
34. Lakshmikantham V., Theory of fractional functional differential equations Nonlinear Analysis 2008 69 10 3337 3343
35. Lakshmikantham V., Vatsala A. S., General uniqueness and monotone iterative technique for fractional differential equations Applied Mathematics Letters 2008 21 8 828 834
36. Liu X., Jia M., Multiple solutions for fractional differential equations with nonlinear boundary conditions Computers and Mathematics with Applications 2010 59 8 2880 2886
37. Lv Z., Liang J., Xiao T., Solutions to the Cauchy problem for differential equations in Banach spaces with fractional order Computers and Mathematics with Applications 2011 62 3 1303 1311
38. McRae F. A., Monotone iterative technique and existence results for fractional differential equations Nonlinear Analysis 2009 71 12 6093 6096
39. Wei Z., Dong W., Che J., Periodic boundary value problems for fractional differential equations involving a Riemann-Liouville fractional derivative Nonlinear Analysis 2010 73 10 3232 3238
40. Wei Z., Li Q., Che J., Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative Journal of Mathematical Analysis and Applications 2010 367 1 260 272
41. Zhang S., Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives Nonlinear Analysis 2009 71 5-6 2087 2093
42. Zhang S., Existence of a solution for the fractional differential equation with nonlinear boundary conditions Computers and Mathematics with Applications 2011 61 4 1202 1208
43. Zhao X., Chai C., Ge W., Positive solutions for fractional four-point boundary value problems Communications in Nonlinear Science and Numerical Simulation 2011 16 9 3665 3672
44. Li Y., Liu Z., Monotone iterative technique for addressing impulsive integro-differential equations in Banach spaces Nonlinear Analysis 2007 66 1 83 92 (Pubitemid 44711922)
45. Chen P., Li Y., Mixed monotone iterative technique for a class of semilinear impulsive evolution equations in Banach spaces Nonlinear Analysis 2011 74 11 3578 3588
46. Chen P., Mixed monotone iterative technique for impulsive periodic boundary value problems in Banach spaces Boundary Value Problems 2011 2011 13
47. Yang H., Mixed monotone iterative technique for abstract impulsive evolution equations in Banach spaces Journal of Inequalities and Applications 2010 2010 15
48. Miller K., Ross B., An introduction to the fractional calculus and fractional differential equations 1993 New York, NY, USA John Wiley and Sons
49. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press Mathematics in Science and Engineering
50. Samko S., Kilbas A., Marichev O., Fractional Integrals and Derivatives: Theory and Applications 1993 Switzerland Gordon and Breach Science
51. Deimling K., Nonlinear Functional Analysis 1985 Berlin, Germany Springer
52. Heinz H. R., On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions Nonlinear Analysis 1983 7 12 1351 1371
53. Ye H., Gao J., Ding Y., A generalized Gronwall inequality and its application to a fractional differential equation Journal of Mathematical Analysis and Applications 2007 328 2 1075 1081
54. Du Y., Fixed points of increasing operators in ordered Banach spaces and applications Applicable Analysis 1990 38 1-2 1 20
55. Campanato S., Generation of analytic semigroups by elliptic operators of second order in H lder spaces Annali della Scuola Normale Superiore di Pisa 1981 8 3 495 512
56. Liang J., Liu J., Xiao T., Nonlocal problems for integrodifferential equations Dynamics of Continuous, Discrete and Impulsive Systems 2008 15 6 815 824