
تعداد نشریات | 21 |
تعداد شمارهها | 610 |
تعداد مقالات | 9,028 |
تعداد مشاهده مقاله | 67,082,917 |
تعداد دریافت فایل اصل مقاله | 7,656,370 |
Controllability of impulsive fractional nonlinear control system with Mittag-Leffler kernel in Banach space | ||
International Journal of Nonlinear Analysis and Applications | ||
دوره 13، شماره 1، خرداد 2022، صفحه 3257-3280 اصل مقاله (459.04 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6080 | ||
نویسندگان | ||
Fadhil Abbas Naji* ؛ Iftichar Al-Sharaa | ||
Department of mathematics, College of Education for Pure Sciences, University of Babylon, Babel, Iraq | ||
تاریخ دریافت: 21 خرداد 1400، تاریخ بازنگری: 31 مرداد 1400، تاریخ پذیرش: 27 مهر 1400 | ||
چکیده | ||
In this paper, we study the controllability of a nonlinear impulsive fractional control system with Mittag-Leffler kernel in Banach space. Firstly, we present the mild solution of the control system using fractional calculus and semigroup theory. We set sufficient conditions to prove the controllability of the control system using the Nussbaum fixed point theorem. Finally, to illustrate our results, an example is given. | ||
کلیدواژهها | ||
Controllability؛ Fractional calculus؛ Mittag-Leffler؛ semigroup theory | ||
مراجع | ||
[1] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, 1993. [2] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204. Elsevier, 2006. [3] I. Podlubny, An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Academic Press, Inc., San Diego CA, 1999. [4] D. Bainov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, CRC Press, 1993. [5] A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, 1995. [6] V. Lakshmikantham and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific, 1989. [7] M. Feˇckan, J.-R. Wang, and Y. Zhou, On the new concept of solutions and existence results for impulsive fractional evolution equations, Dyn. Partial Differ. Equ. 8(4 ) (2011) 345–361. [8] K. Balachandran and S. Kiruthika, Existence of solutions of abstract fractional impulsive semilinear evolution equations, Electron. J. Qual. Theory Differ. Equ. 2010(4) (2010) 1–12. [9] M. Benchohra and B.A. Slimani, Existence and uniqueness of solutions to impulsive fractional differential equations, Electron. J. Differ. Equ. 2009(1) (2009) 1–11. [10] A. Debbouche and D. Baleanu, Controllability of fractional evolution nonlocal impulsive quasilinear delay integrodifferential systems, Comput. Math. Appl. 62(3) (2011) 1442–1450. [11] H. Qin, X. Zuo and J. Liu, Existence and controllability results for fractional impulsive integrodifferential systems in Banach spaces, Abstr. Appl. Anal. 2013 (2013). [12] V.S. Muni and R.K. George, Controllability of semilinear impulsive control systems with multiple time delays in control, IMA J. Math. Control Inf. 36(3) (2019) 869–899. [13] K. Hattaf, A new generalized definition of fractional derivative with non-singular kernel, Comput. 8(2) (2020) 49. [14] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44. Springer Science & Business Media, 2012. [16] Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl. 59(3) (2010) 1063–1077. [17] R.D. Nussbaum, The fixed point index and asymptotic fixed point theorems for k-set-contractions, Bull. Am. Math. Soc. 75(3) (1969) 490–495. [18] R.F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, vol. 21. Springer Science & Business Media, 2012. | ||
آمار تعداد مشاهده مقاله: 15,834 تعداد دریافت فایل اصل مقاله: 350 |