Abstract In this paper, our formulation generalizes the fractional power series to the matrix form and a new version of the matrix fractional Taylor’s series is also considered in terms of Caputo’s fractional derivative. Moreover, several significant results have been realignment to these generalizations. Finally, to demonstrate the capability and efficiency of our theoretical results, we present the solutions of three linear non-homogenous higher order (m − 1 < α ≤ m, m ∈ N) matrix fractional differential equations by using our new approach.

中文翻译：

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一类线性非齐次高阶矩阵分数阶微分方程：解析解与新技术

摘要 在本文中，我们的公式将分数幂级数推广到矩阵形式，并根据 Caputo 分数阶导数考虑了矩阵分数泰勒级数的新版本。此外，一些重要的结果已经重新调整到这些概括。最后，为了证明我们的理论结果的能力和效率，我们通过使用我们的新方法提出了三个线性非齐次高阶 (m − 1 < α ≤ m, m ∈ N) 矩阵分数阶微分方程的解。