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# The Existence and Uniqueness of Solution for Fractional Order Matrix Differential Equation

Xiaoxu Chen

Zibo Vocational Institute, 255314, China.

*Corresponding author: Xiaoxu Chen

Published: 16 November 2022 How to cite this paper

### Abstract

Due to the introduction of fractional calculus which is a generalization of ordi-nary (integer order) differentiation and integration to its fractional (non-integer) order counter- part, almost every problem in calculus can be revisited at a whole new level, where one does not necessarily restrict oneself to an integer order derivative or integral, which allows much more flexibility in solving real-life problems. We are motivated by the article of (Al-Zhour, 2005), in this article the biggest bright spot is that method of Kronecker products of matrices and the method of vector operators. This method of proof not mentioned in the previous knowledge, but it is not restricted by fractional order, and reduce the difficulty of solving equation which is known. It makes the unknown knowledge through variable substitution into the known knowledge, which is very easy to promote. Since previous studies did not give any method of solving matrix fractional dif-ferential equations and the formula, the solving process is too complicated and difficult. Formulas are concluded in this paper, and we also provide strict prove.

KEYWORDS: Kronecker products, Vector-operator, Mittag-Leffler matrix, Matrix fractional differential systems

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### How to cite this paper

Xiaoxu Chen. The Existence and Uniqueness of Solution for Fractional Order Matrix Differential Equation. OA Journal of Education Research, 2022, 1(4), 297-309.