Open Access

Exact controllability of fractional neutral integro-differential systems with state-dependent delay in Banach spaces


Cite

[1] D. Baleanu, J. A. T. Machado, A. C. J. Luo, Fractional Dynamics and Control, Springer, New York, USA, 2012.10.1007/978-1-4614-0457-6Search in Google Scholar

[2] A. Kilbas, H. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amesterdam, 2006.Search in Google Scholar

[3] G. Bonanno, R. Rodriguez-Lopez, S. Tersian, Existence of solutions to boundary value problem for impulsive fractional differential equations, Fractional Calculus and Applied Analysis, 17(3)(2014), 717-744.10.2478/s13540-014-0196-ySearch in Google Scholar

[4] R. Rodriguez-Lopez and S. Tersian, Multiple solutions to boundary value problem for impulsive fractional differential equations, Fractional Calculus and Applied Analysis, 17(4)(2014), 1016-1038.10.2478/s13540-014-0212-2Search in Google Scholar

[5] R. P. Agarwal, V. Lupulescu, D. O'Regan and G. Rahman, Fractional calculus and fractional differential equations in nonreexive Banach spaces, Communications in Nonlinear Science and Numerical Simulation, 20(1)(2015), 59-73.10.1016/j.cnsns.2013.10.010Search in Google Scholar

[6] E. Keshavarz, Y. Ordokhani and M. Razzaghi, Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations, Applied Mathematical Modelling, 38(2014), 6038-6051.10.1016/j.apm.2014.04.064Search in Google Scholar

[7] Z. Lv and B. Chen, Existence and uniqueness of positive solutions for a fractional switched system, Abstract and Applied Analysis, Volume 2014 (2014), Article ID 828721, 7 pages.10.1155/2014/828721Search in Google Scholar

[8] Y. Wang, L. Liu and Y. Wu, Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters, Advances in Difference Equations, 2014:268, 1-24.10.1186/1687-1847-2014-268Search in Google Scholar

[9] B. Ahmad, S. K. Ntouyas and A. Alsaed, Existence of solutions for fractional q-integro-difference inclusions with fractional q-integral boundary conditions, Advances in Difference Equations, 2014:257, 1{18.10.1186/1687-1847-2014-257Search in Google Scholar

[10] R. P. Agarwal, B. D. Andrade, On fractional integro-differential equations with state-dependent delay, Comp. Math. App., 62(2011), 1143{1149.10.1016/j.camwa.2011.02.033Search in Google Scholar

[11] M. Benchohra, F. Berhoun, Impulsive fractional differential equations with state-dependent delay, Commun. Appl. Anal., 14(2)(2010), 213{224.Search in Google Scholar

[12] K. Aissani and M. Benchohra, Fractional integro-differential equations with state-dependent delay, Advances in Dynamical Systems and Applications, 9(1)(2014), 17-30.Search in Google Scholar

[13] J. Dabas and G.R. Gautam, Impulsive neutral fractional integro- differential equation with state-dependent delay and integral boundary condition, Electronic Journal of Differential Equations, Vol. 2013 (2013), No. 273, 1{13.Search in Google Scholar

[14] S. Suganya, M. Mallika Arjunan, and J. J. Trujillo, Existence results for an impulsive fractional integro-differential equation with state-dependent delay, Applied Mathematics and Computation, 266(2015), 54-69.10.1016/j.amc.2015.05.031Search in Google Scholar

[15] J. P. C. Dos Santos, C. Cuevas, B. de Andrade, Existence results for a fractional equations with state-dependent delay, Advances in Difference Equations, (2011), 1-15.10.1155/2011/642013Search in Google Scholar

[16] J. P. C. Dos Santos, M. Mallika Arjunan, and C. Cuevas, Existence results for fractional neutral integro-differential equations with state-dependent delay, Comput. Math. Appl., 62(2011), 1275{1283.10.1016/j.camwa.2011.03.048Open DOISearch in Google Scholar

[17] Z. Yan, Approximate controllability of fractional neutral integro- differential inclusions with state-dependent delay in Hilbert spaces, IMA Journal of Mathematical Control and Information, 30(2013), 443{462.10.1093/imamci/dns033Open DOISearch in Google Scholar

[18] Z. Yan and X. Jia, Approximate controllability of partial fractional neutral stochastic functional integro-differential inclusions with state- dependent delay, Collect. Math., 66(2015), 93{124.10.1007/s13348-014-0109-8Search in Google Scholar

[19] V. Vijayakumar, C. Ravichandran and R. Murugesu, Approximate controllability for a class of fractional neutral integro-differential inclusions with state-dependent delay, Nonlinear Studies, 20(4)(2013), 513-532.Search in Google Scholar

[20] R. P. Agarwal, J. P. C. Dos Santos, and C. Cuevas, Analytic resolvent operator and existence results for fractional integro-differential equations, J. Abstr. Differ. Equ. Appl., 2(2)(2012), 26-47.Search in Google Scholar

[21] V. Vijayakumar, A. Selvakumar and R. Murugesu, Controllability for a class of fractional neutral integro-differential equations with unbounded delay, Applied Mathematics and Computation, 232(2014), 303-312.10.1016/j.amc.2014.01.029Search in Google Scholar

[22] B. D. Andrade, J. P. C. Dos Santos, Existence of solutions for a fractional neutral integro-differential equation with unbounded delay, Electronic Journal of Differential Equations, Vol. 2012 (2012), No. 90, pp. 1{13.Search in Google Scholar

[23] J. P. C. Dos Santos, V. Vijayakumar and R. Murugesu, Existence of mild solutions for nonlocal Cauchy problem for fractional neutral integro-differential equation with unbounded delay, Communications in Mathematical Analysis, X(2011), 1{13.Search in Google Scholar

[24] X. Shu and Q. Wang, The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1 <α< 2, Comput. Math. Appl., 64(2012), 2100{2110.10.1016/j.camwa.2012.04.006Open DOISearch in Google Scholar

[25] Z. Yan and X. Jia, Impulsive problems for fractional partial neutral functional integro-differential inclusions with infinite delay and analytic resolvent operators, Mediterr. Math., 11(2014), 393{428.10.1007/s00009-013-0349-ySearch in Google Scholar

[26] Z. Yan and F. Lu, On approximate controllability of fractional stochastic neutral integro-differential inclusions with infinite delay, Applicable Analysis, (2014), 1235-1258.10.1080/00036811.2014.924214Search in Google Scholar

[27] L. Kexue, P. Jigen, G. Jinghuai, Controllability of nonlocal fractional differential systems of order 2 (1; 2] in Banach spaces, Rep. Math. Phys. , 71(2013), 33{43.10.1016/S0034-4877(13)60020-8Search in Google Scholar

[28] R. Sakthivel, R. Ganesh, Y. Ren, S. Marshal Anthoni, Approximate controllability of nonlinear fractional dynamical systems, Commun. Nonlinear Sci. Numer. Simulat., 18(2013), 3498{3508.10.1016/j.cnsns.2013.05.015Open DOISearch in Google Scholar

[29] C. Rajivganthi, P. Muthukumar. and B. Ganesh Priya, Approximate controllability of fractional stochastic integro-differential equations with infinite delay of order 1<α<2, IMA Journal of Mathematical Control and Information, (2015), 1-15, Available On line.10.1093/imamci/dnv005Search in Google Scholar

[30] J. Dabas and A. Chauhan, Existence and uniqueness of mild solution for an impulsive fractional integro-differential equation with infinite delay, Mathematical and Computer Modelling, 57(3-4)(2013), 754-763.10.1016/j.mcm.2012.09.001Search in Google Scholar

[31] J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21(1978), 11-41.Search in Google Scholar

[32] Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Unbounded Delay, Springer-Verlag, Berlin, 1991.10.1007/BFb0084432Search in Google Scholar

[33] X. Fu and R. Huang, Existence of solutions for neutral integro-differential equations with state-dependent delay, Appl. Math. Comp., 224(2013), 743-759.10.1016/j.amc.2013.09.010Search in Google Scholar

[34] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.10.1007/978-1-4612-5561-1Search in Google Scholar

[35] N. I. Mahmudov and A. Denker, On controllability of linear stochastic systems, Int. J. Control, 73(2000), 144-151.10.1080/002071700219849Search in Google Scholar

eISSN:
1844-0835
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Mathematics, General Mathematics