Approximate controllability of fractional stochastic differential inclusions with nonlocal conditions

References

• Chang YK, Nieto JJ, Li WS. Controllability of semilinear differential systems with non-local initial conditions in Banach spaces. J. Optim. Theor. Appl. 2009;142:267–273.
   Web of Science ®Google Scholar
• Górniewicz L, Ntouyas SK, O’Regan D. Existence and controllability results for first and second order functional semilinear differential inclusions with nonlocal conditions. Numer. Funct. Anal. Optim. 2007;28:53–82.
   Web of Science ®Google Scholar
• Górniewicz L, Ntouyas SK, O’Regan D. Controllability results for first and second order evolution inclusions with nonlocal conditions. Ann. Pol. Math. 2006;89:65–101.
   Google Scholar
• Klamka J. Constrained controllability of semilinear systems with delays. Nonlinear Dyn. 2009;56:169–177.
   Web of Science ®Google Scholar
• Mahmudov NI. Exact null controllability of semilinear evolution systems. J. Global Optim. 2013;56:317–326.
   Web of Science ®Google Scholar
• Ahmed NU. Nonlinear stochastic differential inclusions on Banach space. Stochastic Anal. Appl. 1994;12:1–10.
   Web of Science ®Google Scholar
• Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Vol. 44. Cambridge: Cambridge University Press; 1992.
   Google Scholar
• Fu X. Approximate controllability for neutral impulsive differential inclusions with nonlocal conditions. J. Dyn. Control Syst. 2011;17:359–386.
   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
• Muthukumar P, Rajivganthi C. Approximate controllability of stochastic nonlinear third-order dispersion equation. Int. J. Robust Nonlinear. 2014;24:585–594.
   Web of Science ®Google Scholar
• Sakthivel R, Ren Y. Approximate controllability of fractional differential equations with state-dependent delay. Results Math. 2013;63:949–963.
   Web of Science ®Google Scholar
• Muthukumar P, Rajivganthi C. Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. J. Control Theor. Appl. 2013;11:351–358.
   Google Scholar
• Agarwal RP, De Andrade B, Siracusa G. On fractional integro-differential equations with state-dependent delay. Comput. Math. Appl. 2011;62:1143–1149.
   Web of Science ®Google Scholar
• Mophou GM, Nakoulima O, N’Guérékata GM. Existence results for some fractional differential equations with nonlocal conditions. Nonlinear Stud. 2010;17:15–22.
   Google Scholar
• Shu XB, Lai Y, Chen Y. The existence of mild solutions for impulsive fractional partial differential equations. Nonlinear Anal.-Theor. 2011;74:2003–2011.
   Web of Science ®Google Scholar
• Cui J, Yan L. Existence result for fractional neutral stochastic integro-differential equations with infinite delay. J. Phys. A: Math. Theor. 2011;44:335201.
   Web of Science ®Google Scholar
• Wang J, Zhou Y. Existence and controllability results for fractional semilinear differential inclusions. Nonlinear Anal.-Real. 2011;12:3642–3653.
   Web of Science ®Google Scholar
• Yan Z. On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces. Ann. Pol. Math. 2011;101:87–104.
   Web of Science ®Google Scholar
• Yan Z, Zhang H. Existence of solutions to impulsive fractional partial neutral stochastic integro-differential inclusions with state-dependent delay. Electron. J. Differ. Equ. 2013;2013:1–21.
   Web of Science ®Google Scholar
• Ren Y, Hu L, Sakthivel R. Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay. J. Comput. Appl. Math. 2011;235:2603–2614.
   Web of Science ®Google Scholar
• Duan S, Hu J, Li Y. Exact controllability of nonlinear stochastic impulsive evolution differential inclusions with infinite delay in Hilbert spaces. Int. J. Nonlinear Sci. Numer. Simul. 2011;12:23–33.
   Web of Science ®Google Scholar
• Debbouche 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
• Debbouche A, Baleanu D. Exact null controllability for fractional nonlocal integro-differential equations via implicit evolution system. J. Appl. Math. 2012;2012. Article ID 931975, 17 pages.
   Web of Science ®Google Scholar
• Wang J, Zhou Y. Complete controllability of fractional evolution systems. Commun. Nonlinear Sci. Numer. Simul. 2012;17:4346–4355.
   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
• 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, Torres DFM. Approximate controllability of fractional nonlocal delay semilinear systems in Hilbert spaces. Int. J. Control. 2013;86:1577–158.
   Web of Science ®Google Scholar
• Kumar S, Sukavanam N. Approximate controllability of fractional order semi-linear systems with bounded delay. J. Differ. Equ. 2012;251:6163–6174.
   Web of Science ®Google Scholar
• Mahmudov NI. Approximate controllability of fractional neutral evolution equations in Banach spaces. Abstr. Appl. Anal. 2013;2013. Article ID 531894, 11 pages.
   Google Scholar
• Sukavanam N, Kumar S. Approximate controllability of fractional order semilinear delay systems. J. Optim. Theor. Appl. 2011;151:373–384.
   Web of Science ®Google Scholar
• Tafesse S, Sukavanam N. Approximate controllability of fractional order retarded semilinear control systems. Int. J. Mod. Nonlinear Theor. Appl. 2013;2:153–160.
   Google Scholar
• Balasubramaniam P, Vembarasan V, Senthilkumar T. Approximate controllability of impulsive fractional integro-differential systems with nonlocal conditions in Hilbert Space. Numer. Funct. Anal. Optim. 2014;35:177–197.
   Web of Science ®Google Scholar
• Yan Z. Approximate controllability of fractional neutral integro-differential inclusions with state-dependent delay in Hilbert spaces. IMA J. Math. Control I. 2013;30:443–462.
   Web of Science ®Google Scholar
• Sakthivel R, Ganesh R, Anthoni SM. Approximate controllability of fractional nonlinear differential inclusions. Appl. Math. Comput. 2013;225:708–717.
   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
• 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, Ganesh R, Ren Y, Anthoni SM. Approximate controllability of nonlinear fractional dynamical systems. Commun. Nonlinear Sci. Numer. Simul. 2013;18:3498–3508.
   Web of Science ®Google Scholar
• Deimling K. Multivalued differential equations. Berlin: De Gruyter; 1992.
   Google Scholar
• Hu S, Papageorgious NS. Handbook of multivalued analysis (theory). Dordrecht: Kluwer Academic; 1997.
   Google Scholar
• Podlubny I. Fractional differential equations,Vol. 198, Mathematics in sciences and engineering. San Diego (CA): Academic Press; 1999.
   Google Scholar
• Dhage BC. Multi-valued mappings and fixed points II. Tamkang J. Math. 2006;37:27–46.
   Google Scholar
• Agarwal RP, Benchohra M, Hamani S. A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 2010;109:973–1033.
   Web of Science ®Google Scholar
• Dabas J, Chauhan A, Kumar M. Existence of the mild solutions for impulsive fractional equations with infinite delay. Int. J. Differ. Equ. 2011;2011. Article ID 793023, 20 pages.
   Google Scholar