Existence and uniqueness of solutions for impulsive fractional differential equations

Applied Mathematics and Computation

Volumn 224, Issue , 2013, Pages 422-431

  Rehman, Mujeeb Ur ^a   Eloe, Paul W ^b  

^a NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY   (Pakistan)

^b UNIVERSITY OF DAYTON   (United States)

Author keywords

Boundary value problems; Fractional calculus; Impulsive equations

Indexed keywords

EXISTENCE AND UNIQUENESS OF SOLUTION; EXISTENCE THEORY; FRACTIONAL CALCULUS; GENERAL METHOD; IMPULSIVE EQUATIONS; IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS;

COMPUTATIONAL METHODS; MATHEMATICAL TECHNIQUES;

BOUNDARY VALUE PROBLEMS;

EID: 84884861596     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.08.088     Document Type: Article

References (17)

1. 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
2. B. Ahmad, and G. Wang A study of an impulsive four-point nonlocal boundary value problem of nonlinear fractional differential equations Comput. Math. Appl. 62 2011 1341 1349
3. K. Diethelm The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type Lecture Notes in Mathematics Series 2010 Springer
4. M. Feçkan, Y. Zhou, and J. Wang On the concept and existence of solution for impulsive fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 17 2012 3050 3060
5. T.L. Guo, and J. Wei Impulsive problems for fractional differential equations with boundary value conditions Comput. Math. Appl. 2012 10.1016/j.camwa.2012.02.006
6. T. Jankowski Positive solutions to second order four-point boundary value problems for impulsive differential equations Appl. Math. Comput. 202 2008 550 561
7. V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov Theory of impulsive differential equations Series in Modern Applied Mathematics vol. 6 1989 World Scientific New Jersey
8. M. Li, and H. Liu An existence result for second-order impulsive differential equations with nonlocal conditions 2010 Discrete Dyn. Nat. Soc. 2010 ID 293846, 9 pp
9. X. Li, F. Chen, and X. Li Generalized anti-periodic boundary value problems of impulsive fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 18 2013 28 41
10. R. Shi, and L. Chen Stage-structured impulsive SI model for pest management Discrete Dyn. Nat. Soc. 2007 2007 ID 97608, 9pp
11. Y. Tian, and J. Henderson Three anti-periodic solutions for second-order impulsive differential inclusions via nonsmooth critical point theory Nonlinear Anal. 75 2012 6496 6505
12. 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
13. G. Wang, B. Ahmad, and L. Zhang Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions Comput. Math. Appl. 62 2011 1389 1397
14. J. Wang, Y. Zhou, and M. Fečkan On recent developments in the theory of boundary value problems for impulsive fractional differential equations Comput. Math. Appl. 64 2012 3008 3020
15. X. Wang Impulsive boundary value problem for nonlinear differential equations of fractional order Comput. Math. Appl. 62 2011 2383 2391
16. J. Yan, A. Zhao, and J.J. Nieto Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems Math. Comput. Model. 40 2004 509 518 (Pubitemid 40172108)
17. S.T. Zavalishchin, and A.N. Sesekin Dynamic Impulse Systems: Theory and Applications 1997 Kluwer Academic Publishers Group, Dordrecht