Controllability of nonlocal non-autonomous neutral differential systems including non-instantaneous impulsive effects in 𝕉n

Velusamy Kavitha 1 , Mani Mallika Arjunan 2 ,Β and Dumitru Baleanu 3
  • 1 Department of Mathematics, School of Sciences, Arts, Media & Management, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore, India
  • 2 Department of Mathematics, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Chennai-600062, Tamil Nadu, India
  • 3 Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Institute of Space Sciences, , 06530, Ankara, Turkey


This manuscript involves a class of first-order controllability results for nonlocal non-autonomous neutral differential systems with non-instantaneous impulses in the space 𝕉n. Sufficient conditions guaranteeing the controllability of mild solutions are set up. Concept of evolution family and Rothe’s fixed point theorem are employed to achieve the required results. A model is investigated to delineate the adequacy of the results.

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  • [1] R. Agarwal, S. Hristova and D.O’Regan, Non-Instantaneous Impulses in Differential Equations, Springer, 2017.

  • [2] S. Anju and Sanjay K. Srivastava, Lyapunov approach for stability of integro-differential equations with non-instantaneous impulse effect, Malaya Journal of Matematik, 4(1)(2016), 119–125.

  • [3] F.S. Acharya, Controllability of second order semilinear impulsive partial neutral functional differential equations with infinite delay, International Journal of Mathematics and Mathematical Sciences, 3(1)(2013), 207–218.

  • [4] L. Bai and J.J. Nieto, Variational approach to differential equations with not instantaneous impulses, Applied Mathematics Letters, 73(2017), 44–48.

  • [5] L. Byszewski, Theorem about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, Journal of Mathematical Analysis and Applications, 162(1991), 494–505.

  • [6] P. Chen, X. Zhang and Y. Li, Existence of mild solutions to partial differential equations with non-instantaneous impulses, Electronic Journal of Differential Equations, 241(2016), 1–11.

  • [7] K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, Journal of Mathematical Analysis and Applications, 179(1993), 630–637.

  • [8] E. Hernandez and D. ORegan, On a new class of abstract impulsive differential equations, Proceedings of the American Mathematical Society, 141(2013), 1641–1649.

  • [9] P. Kumar, D.N. Pandey, D. Bahuguna, On a new class of abstract impulsive functional differential equations of fractional order, Journal of Nonlinear Sciences and Applications, 7(2014), 102–114.

  • [10] H. Leiva, Rothe’s fixed point theorem and controllability of semilinear non-autonomous systems, Systems & Control Letters, 67(2014), 14–18.

  • [11] H. Leiva, Controllability of semilinear impulsive non-autonomous systems, International Journal of Control, 88(3)(2015), 585–592.

  • [12] M. Malik, R. Dhayal, S. Abbas and A. Kumar, Controllability of non-autonomous nonlinear differential system with non-instantaneous impulses, RASCAM, 113(1)(2019), 103–118.

  • [13] M. Pierri, D. ORegan and V. Rolnik, Existence of solutions for semi-linear abstract differential equations with non instantaneous impulses, Applied Mathematics and Computation, 219(2013), 6743–6749.

  • [14] R. Poongodi, V. T. Suveetha and S. Dhanalakshmi, Existence of mild solutions to partial neutral differential equations with non-instantaneous impulses, Malaya Journal of Matematik, 7(1)(2019), 27–33.

  • [15] S. Selvarasu, P. Kalamani and M. Mallika Arjunan, Approximate controllability of nonlocal impulsive fractional neutral stochastic integrodifferential equations with state-dependent delay in Hilbert spaces, Malaya Journal of Matematik, 4(4)(2016), 571–598.

  • [16] J. Wang and X. Li, Periodic BVP for integer/fractional order nonlinear differential equations with non-instantaneous impulses, Journal of Applied Mathematics and Computing, 46(2014), 321–334.

  • [17] J. Wang and M. Feckan, A general class of impulsive evolution equations, Topological Methods in Nonlinear Analysis, 46(2015), 915–933.


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