Page 238 - Mathematical Techniques of Fractional Order Systems

Controllability of Single-valued Chapter | 7 227

Balder, E.J., 1987. Necessary and sufficient conditions for l1-strong-weak lower semicontinuity
of integral functionals. Nonlinear Anal. Theory Methods Applicat. 11 (12), 1399 1404.
Da Prato, G., Zabczyk, J., 2014. Stochastic Equations in Infinite Dimensions. Cambridge
University Press, Cambridge.
Deimling, K., 1992. Multivalued Differential Equations, Vol. 1. Walter de Gruyter, Berlin.
Dos Santos, J., Vijayakumar, V., Murugesu, R., et al., 2013. Existence of mild solutions for non-
local cauchy problem for fractional neutral integro-differential equation with unbounded
delay. Commun. Math. Anal. 14 (1), 59 71.
El-Sayed, A.M., Ibrahim, A., 1995. Multivalued fractional differential equations. Appl. Math.
Comput. 68 (1), 15 25.
Fan, Z., Mophou, G., 2014. Existence of optimal controls for a semilinear composite fractional
relaxation equation. Rep. Math. Phys. 73 (3), 311 323.
Fitzpatrick, P., Petryshyn, W., 1974. Fixed point theorems for multivalued noncompact acyclic
mappings. Pacif. J. Math. 54 (2), 17 23.
Hale, J.K., Kato, J., 1978. Phase space for retarded equations with infinite delay. Funkcial.
Ekvac 21 (1), 11 41.
Henderson, J., Ouahab, A., 2010. Impulsive differential inclusions with fractional order.
Comput. Math. Appl. 59 (3), 1191 1226.
Herna ´ndez, E., ORegan, D., Balachandran, K., 2010. On recent developments in the theory of
abstract differential equations with fractional derivatives. Nonlinear Anal. Theory Methods
Applicat. 73 (10), 3462 3471.
Herna ´ndez, E., ORegan, D., Balachandran, K., 2013. Existence results for abstract fractional dif-
ferential equations with nonlocal conditions via resolvent operators. Ind. Math. 24 (1),
68 82.
Hu, S.P., 1997. Ns-handbook of multivalued analysis, vol. i.
Kamenskii, M.I., Obukhovskii, V.V., Zecca, P., 2001. Condensing Multivalued Maps and
Semilinear Differential Inclusions in Banach Spaces., Vol. 7. Walter de Gruyter, Berlin.
Kexue, L., Jigen, P., 2012. Fractional resolvents and fractional evolution equations. Appl. Math.
Lett. 25 (5), 808 812.
Li, K., Peng, J., Jia, J., 2012. Cauchy problems for fractional differential equations with rie-
mann liouville fractional derivatives. J. Funct. Anal. 263 (2), 476 510.
Li, Y., Liu, B., 2007. Existence of solution of nonlinear neutral stochastic differential inclusions
with infinite delay. Stochastic Anal. Applicat. 25 (2), 397 415.
Liu, X., Liu, Z., Han, J., 2013. The solvability and optimal controls for some fractional impul-
sive equation, Abstract and Applied Analysis., Vol. 2013. Hindawi Publishing Corporation.
Lizama, C., 2000. Regularized solutions for abstract volterra equations. J. Math. Anal. Applicat.
243 (2), 278 292.
Lizama, C., N’Gue ´re ´kata, G.M., 2013. Mild solutions for abstract fractional differential equa-
tions. Applicable Analysis 92 (8), 1731 1754.
Lizama, C., Poblete, F., 2012. On a functional equation associated with ( )-regularized resolvent
families, Abstract and Applied Analysis, Vol. 2012. Hindawi Publishing Corporation.
Losta, A., Opial, Z., 1965. Application of the kakutani-ky-fan theorem in the theory of ordinary
differential equations or noncompact acyclic-valued map. Bull. Acad. Pol. Sci., Se ´r. Sci.
Math. Astron. Phys 13, 781 786.
Mahmudov, N., Zorlu, S., 2003. Controllability of non-linear stochastic systems. Int. J. Control
76 (2), 95 104.
Mao, X., 2007. Stochastic Differential Equations and Applications. Elsevier.