The present work introduces the k-incomplete second Appell hypergeometric matrix functions for positive real values of k. It establishes various generalized properties related to integral representations and differential relations. Furthermore, as an application of the newly introduced k-incomplete second Appell hypergeometric matrix functions, several new analytical results associated with fractional kinetic equations are established. Moreover, the obtained results may serve as a useful foundation for further investigations in fractional calculus, matrix analysis, and their applications in mathematical physics.