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September 10, 2025Bulletin of Mathematical Sciences4 citationsOpen Access

Representation of solutions to a linear matrix first-order differential equation with delay

Key Points

A formula for solving linear matrix delayed differential equations has been derived, improving prior methods.
This approach discusses commutativity conditions necessary for finding solutions to the initial problem.
The study reveals previously unaddressed open problems in the field of linear differential equations.
Applications are significant in areas where time delays affect system behaviors, suggesting areas for further research.

Abstract

Linear matrix delayed differential equation Formula: see text is dealt with, where Formula: see text is a delay, Formula: see text is an independent variable, Formula: see text is an Formula: see text unknown variable matrix, Formula: see text and Formula: see text are given Formula: see text constant matrices, and Formula: see text is a given Formula: see text variable matrix. Under some commutativity conditions, a formula is derived for solving an initial problem Formula: see text, Formula: see text, where Formula: see text is an Formula: see text variable matrix. Previous results are discussed and open problems for further investigations suggested.

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