On the generalized Apostol-Kolodner differential equation of the second-order

Mustapha Rachidi; Mohammed Mouniane

doi:10.5269/bspm.65373

Mustapha Rachidi Federal University of Mato Grosso do Sul - UFMS https://orcid.org/0000-0002-8210-7383
Mohammed Mouniane Ibn Tofail University https://orcid.org/0000-0001-7150-1273

Resumo

This paper concerns another approach for solving the matrix differential equations of the second order $X''(t)=AX'(t)+BX(t)$, where $A$, $B$ are square matrices of order ${d\times d}$. Such approach is based on some properties of matrix square root and the linear difference equation. We establish various new results and explicit formulas for the solutions of this type of matrix differential equations. Moreover, because of the non-commutativity condition between $A$ and $B$, the matrix fundamental system will play an important role. Finally, our results and their robustness, are validated by providing some examples and applications.

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Biografia do Autor

Mustapha Rachidi, Federal University of Mato Grosso do Sul - UFMS

Institute of Mathematics - INMA

Mohammed Mouniane, Ibn Tofail University

Department of Mathematics

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