  The recurrence matrix relations, differentiation formulas, and analytical and
fractional integral properties of incomplete gamma matrix functions $\gamma(Q,
x)$ and $\Gamma(Q, x)$ are all covered in this article. The generalized
incomplete exponential matrix functions with their integral representations
functions have been examined, along with some relevant characteristics of these
functions such as integral representations functions . Additionally, the
infinite summation relations and formulas for two sequences are shown, along
with the generalized incomplete exponential matrix functions with the integral
representation, addition formula for addition of two arguments, multiplication
formula for multiplication of two arguments, and recurrence matrix relation.
