## VARIATION FORMULAS OF SOLUTION FOR A CONTROLLED FUNCTIONAL-DIFFERENTIAL EQUATION CONSIDERING DELAY PERTURBATION

## VARIATION FORMULAS OF SOLUTION FOR A CONTROLLED FUNCTIONAL-DIFFERENTIAL EQUATION CONSIDERING DELAY PERTURBATION

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*Tamaz Tadumadze Abdeljalil Nachaoui *

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## Abstract

Variation formulas of solution are proved for a controlled non-linear functional-differential equation with constant delay and the continuous initial condition. In this paper, the essential novelty is the effect of delay perturbation in the variation formulas.The continuity of the initial condition means that the values of the initial function and the trajectory always coincide at the initial moment.

## Keywords

Controlled delay functional-differential equation, variation formula of solution, effect of delay perturbation, continuous initial condition.