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Trajectory controllability of integro-differential system of fractional orders in Hilbert spaces

             10. George RK, Chalishajar DN, Nandakumaran      25. Vijayakumar V. Approximate controllability re-
                AK. Exact controllability of the nonlinear third-  sults for non-densely defined fractional neutral
                order dispersion equation. J Math Anal Appl.      differential inclusions with Hille-Yosida operators.
                2007;332(2):1028-1044.                            Int J Control. 2019;92(9):2210-2222.
             11. Nandakumaran AK, George RK. Partial ex-      26. Vijayakumar V. Approximate controllability for
                act  controllability  of  a  non-linear  system.  a class of second-order stochastic evolution in-
                Revista Matemat Univers Complut Madrid            clusions of Clarke’s subdifferential type. Result
                1995;8(N1):181-196.                               Math. 2018a; 73(1):42.
             12. Miller KS, Ross B. An Introduction to the Frac-  27. Vijayakumar V. Approximate controllability re-
                tional Calculus and Fractional Differential Equa-  sults for impulsive neutral differential inclusions
                tions, A Wiley-Interscience Publication. New      of Sobolev-type with infinite delay. Int J Control.
                York: Wiley; 1993.                                2018b;91(10): 2366-2386.
             13. Cardetti F, Gordina M. A note on local control-  28. Matar M. Controllability of fractional semilinear
                lability on Lie groups. Syst Control Lett. 2008;  mixed Volterra-Fredholm integrodifferential equa-
                57(12):978-979.                                   tions with nonlocal conditions. Int J Math Anal.
             14. Muslim M, Kumar A. Controllability of frac-      2010;4(23):1105-1116.
                tional differential equation of order α ∈ (1, 2]  29. Wang J, Zhou Y. A class of fractional evolution
                with non-instantaneous impulses. Asian J Con-     equations and optimal controls. Nonlinear Anal
                trol. 2018;20(2):935-942.                         Real World Appl. 2011;12(1):262-272.
             15. Shukla A, Arora U, Sukavanam N. Approximate  30. Zhou Y, Jiao F. Existence of mild solutions for
                controllability of retarded semilinear stochastic  fractional neutral evolution equations. Comput
                system with non local conditions. J Appl Math     Math Applicat. 2010;59(3):1063-1077.
                Comput. 2015; 49:513-527.                     31. Kumar S, Sukavanam N. Approximate controlla-
             16. Shukla A, Sukavanam N, Pandey DN, Arora U.       bility of fractional order semilinear systems with
                Approximate controllability of second-order semi-  bounded delay. J Differ Equat. 2012;252(11):6163-
                linear control system. Circ Syst Signal Process.  6174.
                2016;35:3339-3354.                            32. Sukavanam N, Kumar S. Approximate controlla-
             17. Wang J, Wei W, Yang Y. Fractional nonlocal in-   bility of fractional order semilinear delay systems.
                tegrodifferential equations and its optimal control  J Optimiz Theor Applicat. 2011;151:373-384.
                in Banach spaces. J Korean Soc Ind Appl Math.  33. Kexue L, Jigen P, Jinghuai G. (2013). Control-
                2010;14(2):79-91.                                 lability of nonlocal fractional differential systems
             18. Jajarmi A, Baleanu D. On the fractional optimal  of order α ∈ (1, 2] in Banach spaces. Rep Math
                control problems with a general derivative opera-  Phys. 2013;71(1):33-43.
                tor. Asian J Control. 2021;23(2): 1062-1071.  34. Arora S, Nandakumaran A. Controllability prob-
             19. Kumar V, Malik M. Total controllability and      lems of a neutral integro-differential equa-
                observability for dynamic systems with non-       tion  with  memory.  arXiv  preprint;  2024.
                instantaneous impulses on time scales. Asian J    arXiv:2407.07886.
                Control. 2021;23(2):847-859.                  35. Jalisraj A, Udhayakumar R. Existence results and
             20. Liu Z, Li X. On the exact controllability of im-  trajectory controllability of conformable Hilfer
                pulsive fractional semilinear functional differen-  fractional neutral stochastic integro-differential
                tial inclusions. Asian J Control. 2015;17(5):1857-  equations. Contemp Math. 2024;5(4):5496-5517.
                1865.                                         36. Shukla A, Sukavanam N, Pandey DN. Approxi-
             21. Dineshkumar C, Udhayakumar R, Vijayakumar        mate controllability of semilinear fractional con-
                V, Nisar KS, Shukla A. A note concerning to       trol systems of order α ∈ (1, 2] with infinite delay.
                approximate controllability of Atangana-Baleanu   Mediterranean J Math. 2016;13:2539-2550.
                fractional neutral stochastic systems with infinite  37. Chalishajar D, Chalishajar H. Trajectory con-
                delay. Chaos Solit Fract. 2022;157: 111916.       trollability of second order nonlinear integro-
             22. Mahmudov NI, Udhayakumar R, Vijayakumar          differential system: an analytical and a numerical
                V. On the approximate controllability of second-  estimation. Differ Equat Dyn Syst. 2015;23:467-
                order evolution hemivariational inequalities. Re-  481.
                sults Math. 2020;75: 1-19.                    38. Chalishajar DN, George RK, Nandakumaran AK,
             23. Mahmudov NI, Murugesu R, Ravichandran C, Vi-     Acharya FS. Trajectory controllability of nonlin-
                jayakumar V. Approximate controllability results  ear integro-differential system. J Franklin Instit.
                for fractional semilinear integro-differential inclu-  2010;347(7):1065-1075.
                sions in Hilbert spaces. Results Math. 2017;71:45-  39. Hariharan R, Udhayakumar R. Approximate con-
                61.                                               trollability for Sobolev-type Fuzzy Hilfer frac-
             24. Shukla A, Vijayakumar V, Nisar KS. A new ex-     tional neutral integro-differential inclusion with
                ploration on the existence and approximate con-   Clarke subdifferential type. Qual Theor Dyn Syst.
                trollability for fractional semilinear impulsive con-  2025;24(1):53.
                trol systems of order r ∈ (1, 2). Chaos Solit Fract.  40. Kumar S, Tajinder. Existence of solution and
                2022;154:111615.                                  optimal control results in coupled wave system
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