Abstract
The substantiation of a possibility of application of partial averaging method on finite interval for differential inclusions with the fuzzy right-hand side with a small parameter is considered.
Highlights
In 1990, Aubin [1] and Baidosov [2, 3] introduced differential inclusions with the fuzzy right-hand side. Their approach is based on usual differential inclusions
The averaging methods combined with the asymptotic representations began to be applied as the basic constructive tool for solving the complicated problems of analytical dynamics described by the differential equations
The scheme offered by Plotnikov et al for a substantiation of schemes of an average of usual differential inclusions [23,24,25,26,27,28] was used
Summary
In 1990, Aubin [1] and Baidosov [2, 3] introduced differential inclusions with the fuzzy right-hand side. In works [21, 22], the possibility of application of schemes of full and partial averaging for differential inclusions with the fuzzy right-hand side, containing a small parameter, was proved. By proving these theorems, the scheme offered by Plotnikov et al for a substantiation of schemes of an average of usual differential inclusions [23,24,25,26,27,28] was used. The possibility of application of partial averaging method for fuzzy differential inclusions without passage to reviewing of separate solutions is proved; that is, all estimations are spent for R-solution corresponding fuzzy systems
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