A Study of Volterra Integro‐Differential Equations Involving Generalized Mittag–Leffler Matrix Function in the Kernels

ABSTRACT In this article, we introduce and investigate a new class of integral operators whose kernels are expressed through the generalized Mittag–Leffler matrix function and the confluent hypergeometric matrix function. We establish the boundedness of these operators in the Lebesgue space and the continuous space . Furthermore, we analyze the composition of these new operators with standard Riemann–Liouville fractional integrals. Subsequently, we formulate a Cauchy‐type problem for a fractional integro‐differential equation with matrix arguments, elegantly reducing it to a Volterra integral equation of the second kind and obtaining its solution via the method of successive approximations. In addition, we present effective computational strategies for the numerical evaluation of these integral operators.