Conditions for the Existence of Local Solutions of Set-Valued Differential Equations with Generalized Derivative

Some remarks on linear set-valued differential equations

“…Now, we consider linear differential equation (3.1) with PS-derivative and BGderivative. By [1,32,33,34,35], this set-valued differential equation (3.1) has at least one solution. Moreover, one of these solutions (the one whose diameter is a non-decreasing function) coincides with the solution of the corresponding differential equation (3.2).…”

One Control Problem for a Set-valued Object

“…A.V. Plotnikov and N.V. Skripnik took advantage of some approaches that were used in [4,14] and introduced a new definition of a derivative, and studied its properties [5][6][7][8][9].…”

“…Now, we consider linear set-valued differential equations 0 ( ) = ( ), T Now, we consider linear set-valued differential equation 1with PS-derivative and BG-derivative. By [5][6][7][8][9][10][11][12], setvalued differential equation 1with PS(BG)-derivative has at least one solution. Moreover, one of these solutions (the one whose diameter is a non-decreasing function) coincides with the solution of the corresponding Hukuhara differential equation and always exists.…”

On differential equations with interval coefficients

“…This derivative is used to solve problems in which uncertainty decreases with time . The next extension of the Hukuhara derivative is generalized derivative concept . This concept is developed by Bede and Gal for fuzzy‐valued functions.…”

“…I‐, II‐, III‐, and IV‐type Hukuhara derivatives are consolidated in one concept, and this generalized derivative concept is used for interval and set‐valued functions. Generalized derivative concept can be implemented for a class of problems where uncertainty increases/decreases with time . The drawback of this derivative arises due to the fact that Hukuhara difference does not exist for any two sets.…”