Fractional finite time delay evolution systems and optimal controls in infinite-dimensional spaces

Journal of Dynamical and Control Systems

Volumn 17, Issue 4, 2011, Pages 515-535

  Wang, Jinrong ^a   Wei, Wei ^a   Zhou, Yong ^b  

^a GUIZHOU UNIVERSITY   (China)

^b XIANGTAN UNIVERSITY   (China)

Author keywords

continuous dependence; existence; Fractional delay evolution system; mild solution; optimal control

Indexed keywords

CONTINUOUS DEPENDENCE; EXISTENCE; FRACTIONAL DELAY; MILD SOLUTION; OPTIMAL CONTROLS;

DELAY CONTROL SYSTEMS; OPTIMIZATION; TIME DELAY;

CONTINUOUS TIME SYSTEMS;

EID: 79961000249     PISSN: 10792724     EISSN: 15738698     Source Type: Journal    
DOI: 10.1007/s10883-011-9128-x     Document Type: Article

References (27)

1. N. U. Ahmed. Semigroup theory with applications to system and control. Longman, New York (1991).
2. A Anguraj P Karthikeyan GM N'Guérékata 2009 Nonlocal Cauchy problem for some fractional abstract differential equations in Banach spaces Commun. Math. Anal. 6 31 35 2465356 1167.34387
3. 1-strong-weak lower semicontinuity of integral functional Nonlin. Anal. 11 1399 1404 917861 0638.49004 10.1016/0362-546X(87)90092-7
4. K Balachandran JY Park 2009 Nonlocal Cauchy problem for abstract fractional semilinear evolution equations Nonlin. Anal. 71 4471 4475 2548677 1213.34008 10.1016/j.na.2009.03.005
5. M Benchohra J Henderson SK Ntouyas A Ouahab 2008 Existence results for fractional order functional differential equations with infinite delay J. Math. Anal. Appl. 338 1340 1350 2386501 1209.34096 10.1016/j.jmaa.2007.06.021
6. M Benchohra J Henderson SK Ntouyas A Ouahab 2008 Existence results for fractional functional differential inclusions with infinite delay and application to control theory Fract. Calc. Appl. Anal. 11 35 56 2379272 1149.26010
7. M Belmekki M Benchohra 2010 Existence results for fractional order semilinear functional differential with nondense domain Nonlin. Anal. 72 925 932 2579358 1179.26018 10.1016/j.na.2009.07.034
8. Y-K Chang V Kavitha M Mallika Arjunan 2009 Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order Nonlin. Anal. 71 5551 5559 2560223 1179.45010 10.1016/j.na.2009.04.058
9. A Chen F Chen S Deng 2010 On almost automorphic mild solutions for fractional semilinear initial value problems Comput. Math. Appl. 59 1318 1325 2579494 1189.34079
10. MM El-Borai 2004 Semigroup and some nonlinear fractional differential equations Appl. Math. Comput. 149 823 831 2033165 1046.34079 10.1016/S0096-3003(03)00188-7
11. L Gaul P Klein S Kempfle 1991 Damping description involving fractional operators Mech. Syst. Signal Process. 5 81 88 10.1016/0888-3270(91)90016-X
12. WG Glockle TF Nonnenmacher 1995 A fractional calculus approach of self-similar protein dynamics Biophys. J. 68 46 53 10.1016/S0006-3495(95)80157-8
13. S. Hu and N. S. Papageorgiou. Handbook of multivalued analysis. Kluwer, Dordrecht-Boston-London (1997).
14. J Henderson A Ouahab 2009 Fractional functional differential inclusions with finite delay Nonlin. Anal. 70 2091 2105 2492146 1159.34010 10.1016/j.na.2008.02.111
15. Hu Lanying Y Ren R Sakthivel 2009 Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays Semigroup Forum 79 507 514 2564060 1184.45006 10.1007/s00233-009-9164-y
16. OK Jaradat A Al-Omari S Momani 2008 Existence of the mild solution for fractional semilinear initial value problems Nonlin. Anal. 69 3153 3159 2452122 1160.34300 10.1016/j.na.2007.09.008
17. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo. Theory and applications of fractional differential equations. In: North-Holland Math. Stud. 204. Elsevier, Amsterdam (2006).
18. N Özdemir D Karadeniz BB Iskender 2009 Fractional optimal control problem of a distributed system in cylindrical coordinates Phys. Lett. A 373 221 226 2488087 10.1016/j.physleta.2008.11.019
19. GM N'Guérékata 2009 Cauchy Problem for some fractional abstract differential equation with nonlocal conditions Nonlin. Anal. 70 1873 1876 1166.34320 10.1016/j.na.2008.02.087
20. GM Mophou GM N'Guérékata 2009 Mild solutions for semilinear fractional differential equations Electron. J. Differ. Equ. 21 1 9
21. GM Mophou GM N'Guérékata 2009 Existence of mild solution for some fractional differential equations with nonlocal conditions Semigroup Forum 79 315 322 2538728 1180.34006 10.1007/s00233-008-9117-x
22. GM Mophou GM N'Guérékata 2010 Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay Appl. Math. Comput. 216 61 69 2596132 1191.34098 10.1016/j.amc.2009.12.062
23. X Xiang H Kuang 2000 Delay systems and optimal controls Acta Math. Appl. Sinica 16 27 35 1757320 1005.49017 10.1007/BF02670961
24. J Wang W Wei Y Yang 2010 Fractional nonlocal integro-differential equations of mixed type with time-varying generating operators and optimal control Opuscula Math. 30 217 234 2669134
25. J Wang W Wei Y Yang 2010 Nonlocal impulsive problems for fractional differential equations with time-varying generating operators in Banach spaces Opuscula Math. 30 361 381 2669125 05924896
26. E. Zeidler. Nonlinear functional analysis and its application. Springer-Verlag, New York (1990).
27. Y Zhou F Jiao 2010 Existence of mild solutions for fractional neutral evolution equations Comput. Math. Appl. 59 1063 1077 2579471 1189.34154