非方的分数阶退化时滞微分方程的通解形式

The explicit representation of solutions for the general fractional degenerate differential equation with delay

随着分数阶微分方程在物理、控制等领域的广泛应用,含有退化因素的分数阶微分方程已成为分数阶微分方程理论的研究热点.主要讨论分数阶退化时滞微分方程的系数矩阵在非方矩阵的情况下方程的转化问题和该方程的通解表达式.首先,利用广义逆矩阵理论给出了系数矩阵不是方阵的分数阶退化时滞微分方程的可以正常化的充要条件.其次,利用Laplace变换方法分别给出了非方的分数阶退化微分方程和非方的分数阶退化时滞微分方程的通解形式.所得结果推广了相关文献的相关结果.

With the wide application of fractional differential system theory in the field of physics,control,etc.,fractional degenerate differential equations have become an important topic in the field of the fractional differential equation.In this paper,the transformation problem and the explicit representation of solution were considered for fractional degradation delay differential equations with non-square matrix.By using the generalized inverse matrix theory,sufficient and necessary conditions that guarantee the general fractional degenerate differential equation with delay were normalized.By combining the fractional Laplace transform method,the explicit representation of solution was derived for fractional degenerate（delay）differential equations.The results generalized the corresponding results of the relevant literature.