Solution of Fractional Differential Equations using Integral Operators with multi-index Mittag-Leffler matrix function in the Kernels

In this article, we introduce a new integral operator associated with multi-index Mittag-Leffler matrix function. We present the boundedness of this operator in the Lebesgue space L(c, d). Furthermore, we analyze the composition of this new operator with standard Riemann-Liouville fractional integral and derivative operators. Subsequently, we formulate first-order Volterra integrodifferential equation involving a multi-index integral operator and obtain its explicit solution using the Laplace transform method. In addition, we present numerical and graphical analysis of the solution to the Volterra integro-differential equation involving the multi-index integral operator. These results enhance the analytical framework of special matrix functions and contribute to the study of fractional integral operators and their applications.