On approximate controllability of fractional stochastic neutral integro-differential inclusions with infinite delay

References

• Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Vol. 204, North-Holland mathematics studies. Amsterdam: Elsevier; 2006.
   Google Scholar
• Podlubny I. Fractional differential equations. Vol. 198, Mathematics in sciences and engineering. San Diego: Academic Press; 1999.
   Google Scholar
• Lakshmikantham V. Theory of fractional differential equations. Nonlinear Anal. 2008;60:3337–3343.
   Web of Science ®Google Scholar
• Benchohra M, Henderson J, Ntouyas SK, Ouahab A. Existence results for fractional functional differential inclusions with infinite delay and application to control theory. Fract. Calc. Appl. Anal. 2008;11:35–56.
   Google Scholar
• El-Borai MM. Some probability densities and fundamental solutions of fractional evolution equations. Chaos Solitons Fract. 2002;14:433–440.
   Web of Science ®Google Scholar
• El-Borai MM. Semigroups and some nonlinear fractional differential equations. Appl. Math. Comput. 2004;149:823–831.
   Web of Science ®Google Scholar
• Yan Z. Existence results for fractional functional integrodifferential equations with nonlocal conditions in Banach spaces. Ann. Pol. Math. 2010;97:285–299.
   Web of Science ®Google Scholar
• Balachandran K, Trujillo JJ. The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces. Nonlinear Anal. 2010;72:4587–4593.
   Web of Science ®Google Scholar
• Santos JPC, Arjunan MM, Cuevas C. Existence results for fractional neutral integro-differential equations with state-dependent delay. Comput. Math. Appl. 2011;62:1275–1283.
   Web of Science ®Google Scholar
• Balachandran K, Park JY. Controllability of fractional integrodifferential systems in Banach spaces. Nonlinear Anal. Hybrid Syst. 2009;3:363–367.
   Web of Science ®Google Scholar
• Debbouchea A, Baleanu D. Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. Comput. Math. Appl. 2011;62:1442–1450.
   Web of Science ®Google Scholar
• Yan Z. Controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay. J. Franklin Inst. 2011;348:2156–2173.
   Web of Science ®Google Scholar
• Liu Z, Li X. On the controllability of impulsive fractional evolution inclusions in Banach spaces. J. Optim. Theory Appl. 2013;156:167–182.
   Web of Science ®Google Scholar
• Triggiani R. A note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J. Control Optim. 1977;15:407–411.
   Web of Science ®Google Scholar
• Sakthivel R, Ren Y, Mahmudov NI. On the approximate controllability of semilinear fractional differential systems. Comput. Math. Appl. 2011;62:1451–1459.
   Web of Science ®Google Scholar
• Kumar S, Sukavanam N. Approximate controllability of fractional order semilinear systems with bounded delay. J. Differ. Equ. 2012;252:6163–6174.
   Web of Science ®Google Scholar
• Yan Z. Approximate controllability of partial neutral functional differential systems of fractional order with state-dependent delay. Int. J. Control. 2012;85:1051–1062.
   Web of Science ®Google Scholar
• Debbouche A, Delfim FM. Torres, Approximate controllability of fractional nonlocal delay semilinear systems in Hilbert spaces. Int. J. Control. 2013;86:1577–1585.
   Web of Science ®Google Scholar
• Mahmudov NI, Denker A. On controllability of linear stochastic systems. Int. J. Control. 2000;73:144–151.
   Web of Science ®Google Scholar
• Mahmudov NI. Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM J. Control Optim. 2003;42:1604–1622.
   Web of Science ®Google Scholar
• Dauer JP, Mahmudov NI. Controllability of stochastic semilinear functional differential equations in Hilbert spaces. J. Math. Anal. Appl. 2004;290:373–394.
   Web of Science ®Google Scholar
• Klamka J. Stochastic controllability of linear systems with state delays. Int. J. Appl. Math. Comput. Sci. 2007;17:5–13.
   Web of Science ®Google Scholar
• Balasubramaniam P, Park JY, Muthukumar P. Approximate controllability of neutral stochastic functional differential systems with infinite delay. Stoch. Anal. Appl. 2010;28:389–400.
   Web of Science ®Google Scholar
• Sakthivel R, Ren Y, Mahmudov NI. Approximate controllability of second-order stochastic differential equations with impulsive effects. Modern Phys. Lett. B. 2010;24:1559–1572.
   Web of Science ®Google Scholar
• Sakthivel R, Ganesh R, Suganya S. Approximate controllability of fractional neutral stochastic system with infinite delay. Rep. Math. Phys. 2012;70:291–311.
   Web of Science ®Google Scholar
• Sakthivel R, Suganya S, Anthoni SM. Approximate controllability of fractional stochastic evolution equations. Comput. Math. Appl. 2012;63:660–668.
   Web of Science ®Google Scholar
• Zang Y, Li J. Approximate controllability of fractional impulsive neutral stochastic differential equations with nonlocal conditions. Bound. Value Probl. 2013;193:1–14.
   Google Scholar
• Muthukumar P, Rajivganthi C. Approximate controllability of fractional order neutral stochastic integro-differential system with nonlocal conditions and infinite delay. Taiwanese J. Math. 2013;17:1693–1713.
   Web of Science ®Google Scholar
• Agarwal RP, Belmekki M, Benchohra M. A survey on semilinear differential equations and inclusions involving riemann-liouville fractional derivative. Adv. Difference Equ. 2009;2009:1–47.
   Google Scholar
• Yan Z. On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces. Ann. Pol. Math. 2011;101:87–103.
   Web of Science ®Google Scholar
• Yan Z, Zhang H. Existence of impulsive fractional partial neutral stochastic integro-differential inclusions with state-dependent delay in Hilbert spaces. Electron. J. Differ. Equ. 2013;2013:1–21.
   Web of Science ®Google Scholar
• O’Regan D. Nonlinear alternatives for multivalued maps with applications to operator inclusions in abstract spaces. Proc. Am. Math. Soc. 1999;127:3557–3564.
   Web of Science ®Google Scholar
• Fitzpatrick PM, Petryshyn WV. Fixed point theorems for multivalued noncompact acyclic mappings. Pacific J. Math. 1974;54:17–23.
   Web of Science ®Google Scholar
• Hale JK, Kato J. Phase spaces for retarded equations with infinite delay. Funkcial. Ekvac. 1978;21:11–41.
   Google Scholar
• Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Cambridge: Cambridge University Press; 1992.
   Google Scholar
• Lasota A, Opial Z. An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 1965;13:781–786.
   Google Scholar
• Hino Y, Murakami S, Naito T. Functional-differential equations with infinite delay. Vol. 1473, Lecture notes in mathematics. Berlin: Springer-Verlag; 1991.
   Google Scholar