Abstract
This research paper aims to introduce an extension of the k-Hurwitz-Lerch zeta-function of matrix arguments and interpret its several properties, like generating matrix relations, derivative formulae, Mellin transforms and integral representations. Further, we discuss the solution of the fractional kinetic equations (FKEs) involving an extended k-Hurwitz-Lerch zeta-function of matrix arguments. In addition, the results investigated in view of an extended k-Hurwitz-Lerch zeta-matrix function are rather general in nature and can easily give various known and novel FKEs.