پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 675 |
| تعداد مقالات | 9,814 |
| تعداد مشاهده مقاله | 69,672,881 |
| تعداد دریافت فایل اصل مقاله | 49,025,812 |
A note on Approximate controllability of differential inclusion with non-instantaneous impulses | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 20 شهریور 1404 اصل مقاله (429.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34305.5122 | ||
| نویسندگان | ||
| Vineet Kumar Chaurasiya1؛ Brijendra Kumar Chaurasiya* 2؛ Avadhesh Kumar2 | ||
| 1Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University Mathura, 281406, India | ||
| 2Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, India | ||
| تاریخ دریافت: 12 خرداد 1403، تاریخ بازنگری: 05 آبان 1403، تاریخ پذیرش: 28 آذر 1403 | ||
| چکیده | ||
| The article explores the study of approximation controllability in a particular subset of differential inclusion systems that include non-instantaneous impulses in the Banach space X. By using non-linear alternatives for Kakutani mappings, semi-group theory, and fixed-point theorems. Our approach yields noteworthy conclusions. Furthermore, we provide a concrete example to clarify how the suggested theoretical framework might be used in practice. An investigation of the concept of approximation controllability is crucial for comprehending the dynamics of a system, especially in situations when attaining exact control is difficult. When we consider systems with impulses that do not happen instantly, we face complexity that requires advanced mathematical techniques for a comprehensive examination. Our study expands the theoretical comprehension of controllability in complex systems and provides valuable insights for both theoretical investigation and practical applications in control theory. | ||
| کلیدواژهها | ||
| Approximate controllability؛ Differential inclusions؛ Non-instantaneous impulses؛ Analytic semi-group | ||
| مراجع | ||
|
[1] N. Abada, M. Benchohra, and H. Hammouche, Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions, J. Differ. Equ. 246 (2009), 3834–3863. [2] K. Balachandran and J.P. Dauer, Controllability of nonlinear systems in Banach spaces: A survey, J. Optim. Theory Appl. 115 (2002), no. 1, 7–28. [3] P. Balasubramaniam and P. Tamilalagan, Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi's function, Appl. Math. Comput. 256 (2015), 232–246. [4] P. Balasubramaniam, V. Vembarasan, and T. Senthilkumar, Approximate controllability of impulsive fractional integro-differential systems with nonlocal conditions in Hilbert space, Numer. Funct. Anal. Optim. 35 (2014), 177–197. [5] M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions: An Introduction to Impulsive Differential Equations and Differential Inclusions of Their Solution and Some of Their Applications, Hindawi Publishing Corporation, 2006. [6] L. Byszewski, Theorem about the existence and uniqueness of solutions of a semilinear nonlocal Cauchy problem, J. Math. Anal Appl. 162 (1991), 494–505. [7] C. Dineshkumar, R. Udhayakumar, V. Vijayakumar, A. Shukla, and K.S. Nisar, New discussion regarding ap[1]proximate controllability for Sobolev-type fractional stochastic hemivariational inequalities of order r ∈(1, 2), Commun. Nonlinear Sci. Numer. Simul. 116 (2023), 106891. [8] C. Dineshkumar, R. Udhayakumar, V. Vijayakumar, and K. Sooppy Nisar, Results on approximate controllability of neutral integro-differential stochastic system with state-dependent delay, Numer. Meth. Partial Differ. Equ. 40 (2024), no. 1, e22698. [9] X. Fu and K. Mei, Approximate controllability of semilinear partial functional differential systems, J. Dyn. Control Syst. 15 (2009), 425–443. [10] M. Guo, X. Xue, and R. Li, Controllability of impulsive evolution inclusions with nonlocal conditions, J. Optim. Theory Appl. 120 (2004), 355–374. [11] E. Hern´andez and D. O’Regan, On a new class of abstract impulsive differential equations, Proc. Am. Math. Soc. 141 (2013), 1641–1649. [12] J. Klamka, Controllability of dynamical systems: A survey, Bull. Polish Acad. Sci. Tech. Sci. 61 (2013), no. 2, 335–342. [13] S. Kumar, K.S. Nisar, R. Kumar, C. Cattani, and B. Samet, A new Rabotnov fractional-exponential function-based fractional derivative for diffusion equation under external force, Math. Meth. Appl. Sci. 43 (2020), no. 7, 4460–4471. [14] P. Kumar, D.N. Pandey, and D. Bahuguna, On a new class of abstract impulsive functional differential equations of fractional order, J. Nonlinear Sci. Appl. 7 (2014), no. 2, 102–114. [15] M. Li and M. Liu, Approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay, Discrete Dyn. Nature Soc. 2015 (2015), no. 1, 420826. [16] N.I. Mahmudov, Approximate controllability of semilinear evolution systems in Hilbert spaces, SIAM. J. Control Optim. 15 (1977), 407–411. [17] M. Muslim, A. Kumar, and M. Feckan, Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses, J. King Saud Univ.-Sci. 30 (2018), no. 2, 204–213. [18] A.D. Myshkis and A.M. Samoilenko, Systems with impulsive at fixed moments of time, Mat. Sb. 74 (1967), 202–208. [19] D.N. Pandey, S. Das, and N. Sukavanam, Existence of solution for a second-order neutral differential equation with state dependent delay and non-instantaneous impulses, Int. J. Nonlinear Sci. 18 (2014), 145–155. [20] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983. [21] R. Sakthivel, R. Ganesh, Y. Ren, and S.M. Anthoni, Approximate controllability of nonlinear fractional dynamical systems, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), no. 12, 3498–3508. [22] R. Sakthivel, N.I. Mahmudov, and J.H. Kim, On controllability of second-order nonlinear impulsive differential systems, Nonlinear Anal. Theory Meth. Appl. 71 (2009), 45–52. [23] A. Shukla and N. Sukavanam, Interior approximate controllability of second-order semilinear control systems, Int. J. Control 97 (2024), no. 3, 615–624. [24] P. Veeresha, D.G. Prakasha, and S. Kumar, A fractional model for propagation of classical optical solitons by using nonsingular derivative, Math. Meth. Appl. Sci. 47 (2024), no. 13, 10609–10623. [25] V. Vijayakumar, C. Ravichandran, K.S. Nisar, and K.D. Kucche, New discussion on approximate controllability results for fractional Sobolev type Volterra-Fredholm integro-differential systems of order 1 < r < 2, Numer. Meth. Partial Differ. Equ. 40 (2024), no. 2, e22772. [26] Z. Yan, Approximate controllability of fractional neutral integro-differential inclusions with state-dependent delay in Hilbert spaces, IMA J. Math. Control Inf. 30 (2013), 443–462. [27] Z. Yan and F. Lu, On approximate controllability of fractional stochastic neutral integro-differential inclusions with infinite delay, Appl. Anal. 94 (2015), 1235–1258. | ||
|
آمار تعداد مشاهده مقاله: 100 تعداد دریافت فایل اصل مقاله: 179 |
||