Controllability of second order neutral impulsive fuzzy functional differential equations with Non-Local conditions
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Keywords:
Controllability, Neutral Impulsive Differential Equation, Banach Fixed Point Theorem, Fuzzy solution, Non-local initial conditions.Abstract
In this paper, the controllability of fuzzy solutions for a second-order nonlocal impulsive neutral functional differential equation with both nonlocal and impulsive conditions in terms of fuzzy are considered. The sufficient condition of controllability is developed using the Banach fixed point theorem and a fuzzy number whose values are normal, convex, upper semi-continuous, and compactly supported fuzzy sets with the Hausdorff distance between α-cuts at its maximum. The α-cut approaches allow to translate a system of fuzzy differential equations into a system of ordinary differential equations to the endpoints of the states. An example of the application is given at the end to demonstrate the results. These kinds of systems come in use for designing landing systems for planes and spacecraft, as well as car suspension systems.
References
Falguni Acharya et al. Controllability of Fuzzy Solutions for Neutral Impulsive Functional Differential Equations with Nonlocal Conditions. In: Axioms 2021, 10(2): 84.
Sumit Arora et al. Approximate controllability of semilinear impulsive functional differential systems with non-local conditions. In: IMA Journal of Mathematical Control and Information 2020, 37(4): 1070–1088.
G Arthi and Ju H Park. On controllability of second-order impulsive neutral integrodifferential systems with infinite delay. In: IMA Journal of Mathematical Control and Information 32(3): (2015), 639–657.
K Balachandran, JY Park, and SH Park. Controllability of nonlocal impulsive quasi-linear integrodifferential systems in Banach spaces. In: Reports on Mathematical Physics 2010, 65(2): 247–257.
Mouffak Benchohra, Juan J Nieto, and Abdelghani Ouahab. Fuzzy solutions for impulsive differential equations. In: Communications in Applied Analysis 11(3–4): (2007), 379–394.
Dimplekumar N Chalishajar, Heena D Chalishajar, and Falguni S Acharya. Controllability of second order neutral impulsive differential inclusions with nonlocal conditions. In: Dyn. Contin., Discrete Impul. Syst. Ser. A, Math. Anal 2012, 19: 107–134.
DN Chalishajar and E Ramesh, Controllability for impulsive fuzzy neutral functional integrodifferential equations. In: AIP Conference Proceedings. 2159(1) AIP Publishing LLC. 2019, 030007.
DN Chalishajar et al. Existence of fuzzy solutions for nonlocal impulsive neutral functional differential equations. In:
Journal of Nonlinear Analysis and Application 2017, 2017(1): 19–30.
Y-K Chang, A Anguraj, and M Mallika Arjunan. Existence results for impulsive neutral functional differential equations with infinite delay. In: Nonlinear Analysis: Hybrid Systems 2008, 2(1): 209–218.
Didier Dubois and Henri Prade. Towards fuzzy differential calculus part 1: Integration of fuzzy mappings. In: Fuzzy sets and Systems 1982, 8(1): 1–17.
Didier Dubois and Henri Prade. Towards fuzzy differential calculus part 2: Integration on fuzzy intervals. In: Fuzzy sets and Systems 1982, 8(2): 105–116.
M Guo, X Xue, and E Li. Controllability of impulsive evolution inclusions with nonlocal conditions. In: Journal of Optimization Theory and Applications 2004, 120(2): 355–374.
JK Hale. Introduction to functional Differential Equations. In: Applied Mathematical Sciences 99 (1993).
Eduardo Hernandez and Hernan E Henriquez. Impulsive partial neutral differential equations. In: Applied Mathematics Letters 2006, 19(3): 215–222.
Eaju K George, Dimplekumar Chalishajar, and A. Nandakumaran. Controllability of Second Order Semi-Linear Neutral Functional Differential Inclusions in Banach Spaces. In: Mediterranean Journal of Mathematics 1 (Jan. 2004), 463–477. DOI: 10.1007/s00009-004-0024-4.
Osmo Kaleva, Fuzzy differential equations. In: Fuzzy sets and systems 1987, 24(3): 301–317.
Mohit Kumar and Sandeep Kumar. Controllability of impulsive second order semilinear fuzzy integrodifferential control systems with nonlocal initial conditions. In: Applied Soft Computing 2016, 39: 251–265.
Vangipuram Lakshmikantham, Pavel S Simeonov, et al. Theory of impulsive differential equations. Vol. 6. World scientific, 1989.
Jianli Li, Periodic boundary value problems for second-order impulsive integro-differential equations. In: Applied mathematics and computation 2008, 198(1): 317–325.
Bing Liu, Controllability of impulsive neutral functional differential inclusions with infinite delay. In: Nonlinear Analysis: Theory, Methods & Applications 2005, 60(8): 1533–1552.
Zadeh Lotfi et al, Fuzzy sets. In: Information and control 1965, 8(3): 338–353.
Jose A Machado et al. Controllability results for impulsive mixed-type functional integro-differential evolution equations with nonlocal conditions. In: Fixed point theory and Applications 2013, 2013(1): 1–16.
Jong Yeoul Park and Hvo Keun Han. Existence and uniqueness theorem for a solution of fuzzy differential equations. In: International Journal of Mathematics and Mathematical Sciences 1999, 22(2): 271–279.
Guixiang Wang, Youming Li, and Chenglin Wen. On fuzzy n-cell numbers and n-dimension fuzzy vectors. In: Fuzzy Sets and Systems 2007, 158(1): 71–84
