On recent developments in the theory of boundary value problems for impulsive fractional differential equations

Computers and Mathematics with Applications

Volumn 64, Issue 10, 2012, Pages 3008-3020

  Wang, Jinrong ^a   Zhou, Yong ^b   Feckan, Michal ^c,d  

^a GUIZHOU UNIVERSITY   (China)

^b XIANGTAN UNIVERSITY   (China)

^c Faculty of Natural Sciences   (Slovakia)

^d INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Boundary value problems; Impulsive fractional differential equations; Solutions

Indexed keywords

CITED PAPERS; DATA DEPENDENCE; FIXED POINT METHODS; GRONWALL INEQUALITY; IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS; SUFFICIENT CONDITIONS;

ALGORITHMS; MATHEMATICAL MODELS; SOLUTIONS;

BOUNDARY VALUE PROBLEMS;

EID: 84868206100     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.12.064     Document Type: Article

References (31)

1. K. Diethelm The analysis of fractional differential equations Lecture Notes in Math. 2010
2. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and applications of fractional differential equations North-Holland Mathematics Studies vol. 204 2006 Elsevier Science B.V Amsterdam
3. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Differential Equations 1993 John Wiley New York
4. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
5. V.E. Tarasov Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media 2010 Springer HEP
6. R.P. Agarwal, M. Benchohra, and S. Hamani A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions Acta. Appl. Math. 109 2010 973 1033
7. B. Ahmad, and J.J. Nieto Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions Comput. Math. Appl. 58 2009 1838 1843
8. Z. Bai On positive solutions of a nonlocal fractional boundary value problem Nonlinear Anal.: TMA 72 2010 916 924
9. M. Benchohra, J. Henderson, S.K. Ntouyas, and A. Ouahab Existence results for fractional order functional differential equations with infinite delay J. Math. Anal. Appl. 338 2008 1340 1350
10. Y.-K. Chang, and J.J. Nieto Some new existence results for fractional differential inclusions with boundary conditions Math. Comput. Modelling 49 2009 605 609
11. M. Feckan, Y. Zhou, and J. Wang On the concept and existence of solution for impulsive fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 2011 10.1016/j.cnsns.2011.11.017
12. J. Wang, and Y. Zhou A class of fractional evolution equations and optimal controls Nonlinear Anal.: RWA 12 2011 262 272
13. J. Wang, and Y. Zhou Analysis of nonlinear fractional control systems in Banach spaces Nonlinear Anal.: TMA 74 2011 5929 5942
14. J. Wang, and Y. Zhou Existence and controllability results for fractional semilinear differential inclusions Nonlinear Anal.: RWA 12 2011 3642 3653
15. S. Zhang Existence of positive solution for some class of nonlinear fractional differential equations J. Math. Anal. Appl. 278 2003 136 148 (Pubitemid 36445950)
16. Y. Zhou, F. Jiao, and J. Li Existence and uniqueness for fractional neutral differential equations with infinite delay Nonlinear Anal.: TMA 71 2009 3249 3256
17. Y. Zhou, and F. Jiao Nonlocal Cauchy problem for fractional evolution equations Nonlinear Anal.: RWA 11 2010 4465 4475
18. B. Ahmad, and S. Sivasundaram Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations Nonlinear Anal.: HS 3 2009 251 258
19. B. Ahmad, and S. Sivasundaram Existence of solutions for impulsive integral boundary value problems of fractional order Nonlinear Anal.: HS 4 2010 134 141
20. B. Ahmad, and G. Wang Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order Comput. Math. Appl. 59 2010 1341 1349
21. Y. Tian, and Z. Bai Existence results for the three-point impulsive boundary value problem involving fractional differential equations Comput. Math. Appl. 59 2010 2601 2609
22. J. Cao, and H. Chen Some results on impulsive boundary value problem for fractional differential inclusions Electron. J. Qual. Theory Differ. Equ. 2010 11 2010 1 24
23. G. Wang, B. Ahmad, and L. Zhang Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order Nonlinear Anal.: TMA 74 2011 792 804
24. G. Wang, L. Zhang, and G. Song Systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions Nonlinear Anal.: TMA 74 2011 974 982
25. G. Wang, B. Ahmad, and L. Zhang Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions Comput. Math. Appl. 59 2010 1389 1397
26. X. Wang Impulsive boundary value problem for nonlinear differential equations of fractional order Comput. Math. Appl. 62 2011 2383 2391
27. J. Cao, and H. Chen Impulsive fractional differential equations with nonlinear boundary conditions Math. Comput. Modelling 2011 10.1016/j.mcm.2011. 07.037
28. L. Yang, and H. Chen Nonlocal boundary value problem for impulsive differential equations of fractional order Adv. Differential Equations 2011 2011 16 Article ID 404917
29. J. Wang, X. Xiang, and Y. Peng Periodic solutions of semilinear impulsive periodic system on Banach space Nonlinear Anal.: TMA 71 2009 e1344 e1353
30. W. Wei, X. Xiang, and Y. Peng Nonlinear impulsive integro-differential equation of mixed type and optimal controls Optimization 55 2006 141 156 (Pubitemid 43688719)
31. I.P. Natanson Theory of Functions of a Real Variable vol. II 1960 Frederick Ungar Publishing Co New York