κ-FRACTIONAL DERIVATIVE OPERATOR AND SOLUTION OF FRACTIONAL KINETIC EQUATIONS INVOLVING (κ,𝔍)-SECOND APPELL HYPERGEOMETRIC MATRIX FUNCTIONS WITH THE TWO VARIABLES

In this study, we present a new definition of [Formula: see text])-second Appell hypergeometric matrix functions ([Formula: see text])-SAHMFs). Then, we investigate analytical properties related to the novel matrix function such as derivative formulas and integral representations, and the [Formula: see text]-fractional derivative operators. Additionally, we obtain bilinear and linear generating relations for the [Formula: see text])-SAHMFs. This work presents novel results regarding [Formula: see text])-SAHMFs to solve the fractional kinetic equations.