Nonlocal Controllability for the Semilinear Fuzzy Integrodifferential Equations in n-Dimensional Fuzzy Vector Space

Abstract

We study the existence and uniqueness of solutions and controllability for the semilinear fuzzy integrodifferential equations in n-dimensional fuzzy vector space E N n by using Banach fixed point theorem, that is, an extension of the result of J. H. Park et al. to n-dimensional fuzzy vector space.

Existence of Solutions for the Impulsive Semilinear Fuzzy Intergrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory in n-dimensional Fuzzy Vector Space(ENn, dε)

“…Gal and N'Guerekata [5] studied almost automorphic fuzzy-number-valued functions. Recently, Kwun et al [9] study the the existence and uniqueness of solutions and nonlocal controllability for the semilinear fuzzy integrodifferential equations in n-dimensional fuzzy vector space.…”

Averaging of Fuzzy Integrodifferential Inclusions

“…The applications of fuzzy set theory can be found in many branches of science as physical, mathematical, differential equations and engineering sciences. Recently there have been new advances in the theory of fuzzy differential equations [12][13][14][15][16], fuzzy integrodifferential equations [17][18][19][20], differential inclusions with fuzzy right-hand side [21][22][23][24] and fuzzy differential inclusions [25][26][27] as well as in the theory of control fuzzy d i f f e r e n t i a l e q u a t i o n s [ 2 8 -3 0 ] , c o n t r o l f u z z y integrodifferential equations [31][32][33][34][35], controlfuzzy differential inclusions [36][37][38][39], and control fuzzy integrodifferential inclusions [40]. In works [41][42][43][44][45][46][47][48] various schemes of an average for the fuzzy differential equations and inclusions have been considered.…”

Existence of Periodic Solutions for Fuzzy Differential Equations

“…Nieto et al [9] proved the existence of solution for the initial value problems associated to the fuzzy equations. Kwun et al [4] proved nonlocal controllability for the semilinear fuzzy integrodifferential equations in n-dimensional fuzzy vector space. Our objective is also throughout the fuzzy systems, the situation is vague and uncertain to enable them to solve mathematical problems.…”