Impulsive fractional partial differential equations

Applied Mathematics and Computation

Volumn 257, Issue , 2015, Pages 581-590

  Guo, Tian Liang ^a   Zhang, KanJian ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

Caputo derivative; Cauchy problem; Impulsive partial differential equations; Measure of noncompactness; M nch's fixed point theorem

Indexed keywords

BANACH SPACES; DIFFERENTIAL EQUATIONS; FIXED POINT ARITHMETIC; FUNCTIONAL ANALYSIS; TOPOLOGY;

CAPUTO DERIVATIVES; CAUCHY PROBLEMS; FIXED POINT THEOREMS; IMPULSIVE PARTIAL DIFFERENTIAL EQUATIONS; MEASURE OF NONCOMPACTNESS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84931560736     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.05.101     Document Type: Article

References (27)

1. Yong Zhou Basic Theory of Fractional Differential Equations 2014 World Scientific Singapore
2. L. Gaul, P. Klein, and S. Kempfle Damping description involving fractional operators Mech. Syst. Signal Process. 5 1991 81 88
3. W.G. Glockle, and T.F. Nonnenmacher A fractional calculus approach of selfsimilar protein dynamics Biophys. J. 68 1995 46 53
4. R. Hilfer Applications of fractional calculus in physics 2000 World Scientific Singapore
5. F. Mainardi Fractional calculus: some basic problems in continuum and statistical mechanics A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer-Verlag Wien 291 348
6. F. Metzler, W. Schick, H.G. Kilian, and T.F. Nonnenmacher Relaxation in filled polymers: a fractional calculus approach J. Chem. Phys. 103 1995 7180 7186
7. I. Podlubny Fractional differential equations 1999 Academic Press San Diego
8. 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
9. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier Science B.V Amsterdam
10. B. Ahmad, and J.J. Nieto Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory Topol. Methods Nonlinear Anal. 35 2010 295 304
11. G.M. Mophou, and G.M. N'Guérékata Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay Appl. Math. Comput. 216 2010 61 69
12. JinRong Wang, and Yong Zhou Analysis of nonlinear fractional control systems in Banach spaces Nonlinear Anal. TMA 74 2011 5929 5942
13. JinRong Wang, and Yong Zhou Existence and controllability results for fractional semilinear differential inclusions Nonlinear Anal. RWA 12 2011 3642 3653
14. Michal Fečkan, Yong Zhou, and JinRong Wang On the concept and existence of solutions for impulsive fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 17 7 2012 3050 3060
15. JinRong Wang, Michal Fečkan, and Yong Zhou On the new concept of solutions and existence results for impulsive fractional evolution equations Dyn. Partial Differ. Equ. 8 4 2011 345 361
16. S. Zhang Existence of positive solution for some class of nonlinear fractional differential equations J. Math. Anal. Appl. 278 2003 136 148
17. Yong Zhou, F. Jiao, and J. Li Existence and uniqueness for fractional neutral differential equations with infinite delay Nonlinear Anal. TMA 71 2009 3249 3256
18. Z.B. Bai On positive solutions of a nonlocal fractional boundary value problem Nonlinear Anal. TMA 72 2010 916 924
19. Aaïd Abbas, and M. Benchohra Impulsive hyperbolic functional differential equations of fractional order with state-dependent delay Fract. Calc. Appl. Anal. 13 2010 225 242
20. Aaïd Abbas, and M. Benchohra Upper and lower solutions method for impulsive hyperbolic differential equations with fractional order Nonlinear Anal. HS 4 2010 406 413
21. Saïd Abbas, Ravi P. Agarwal, and Mouffak Benchohra Darboux problem for impulsive partial hyperbolic differential equations of fractional order with variable times and infinite delay Nonlinear Anal. HS 4 2010 818 829
22. Saïd Abbas, Mouffak Benchohra, and Lech Gorniewicz Existence theory for impulsive partial hyperbolic functional differential equations involving the Caputo fractional derivative Sci. Math. Jpn. 72 1 2010 49 60
23. M. Benchohra, and D. Seba Impulsive partial hyperbolic fractional order differential equations in banach spaces J. Fract. Calc. Appl. 1 4 2011 1 12
24. A.N. Vityuk, and A.V. Golushkov Existence of solutions of systems of partial differential equations of fractional order Nonlinear Oscil. 7 3 2004 318 325
25. J. Bans, and K. Goebel Measures of Noncompactness in Banach Spaces 1980 Marcel Dekker New York
26. H. Mönch Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces Nonlinear Anal. 4 1980 985 999
27. S. Abbas, G.M. N'Guerekata, and M. Benchohra Topics in Fractional Differential Equations 2012 Springer