Solution of Fractional Kinetic Equations Involving New Extended Incomplete Second Appell Hypergeometric Matrix Functions

In this paper, we introduce a new extension of the incomplete second Appell hypergeometric matrix functions (EISAHMFs) and extension of the second Appell hypergeometric matrix functions (ESAHMFs) in terms of the extended incomplete Pochhammer matrix symbols and extended Pochhammer matrix symbols, respectively. Firstly, we define an extension of the EISAHMFs and ESAHMFs. Subsequently, we investigate integral representations, differential formulas, transformation formulas, and recurrence relations pertaining to EISAHMFs. Then, we present the Mellin matrix transform of the ESAHMFs. Finally, a new result regarding the solution of the fractional kinetic equations in the terms of newly ESAHMFs is discussed.