Abstract
We study the existence and uniqueness of solutions and nonlocal controllability for the impulsive semilinear nonlocal fuzzy integrodifferential equations in -dimensional fuzzy vector space by using short-term perturbations techniques and Banach fixed point theorem. This is an extension of the result of Kwun et al. (Kwun et al., 2009) to impulsive system.
Highlights
The theory of differential equations with discontinuous trajectories during the last twenty years has been to a great extent stimulated by their numerous applications to problem arising in mechanics, electrical engineering, the theory of automatic control, medicine and biology
Rogovchenko 4 followed the ideas of the theory of impulsive differential equations which treats the changes of the state of the evolution process due to a short-term perturbations whose duration can be negligible in comparison with the duration of the process as an instant impulses
We study the existence and uniqueness of solutions and nonlocal controllability for the following impulsive semilinear nonlocal fuzzy integrodifferential equations in n-dimensional fuzzy vector space by using short-term perturbations techniques and Banach fixed point theorem: dxi t dt
Summary
The theory of differential equations with discontinuous trajectories during the last twenty years has been to a great extent stimulated by their numerous applications to problem arising in mechanics, electrical engineering, the theory of automatic control, medicine and biology. Park et al 6 studied the existence and uniqueness of fuzzy solutions and controllability for the impulsive semilinear fuzzy integrodifferential equations in onedimensional fuzzy vector space EN1. In one-dimensional fuzzy vector space EN1 , Park et al 9 proved the existence and uniqueness of fuzzy solutions and presented the sufficient condition of nonlocal controllability for the following semilinear fuzzy integrodifferential equation with nonlocal initial condition. Kwun et al studied the existence and uniqueness of solutions and nonlocal controllability for the semilinear fuzzy integrodifferential equations in n-dimensional fuzzy vector space. We study the existence and uniqueness of solutions and nonlocal controllability for the following impulsive semilinear nonlocal fuzzy integrodifferential equations in n-dimensional fuzzy vector space by using short-term perturbations techniques and Banach fixed point theorem: dxi t dt. 0, ui : 0, T → ENi bounded functions, is a Δxi control tk xi ftukn−ctxioi nt,−kx,0wi ∈heEreNi xiis an t−k and xi tk represent the left and right limits of xi t at t tk, respectively
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