On the solutions of certain fractional kinetic matrix equations involving Hadamard fractional integrals

Currently, matrix fractional differential equations have several applications in diverse fields, including mathematical analysis, control systems, economics, optimization theory, physics, astrophysics and engineering. In this line of research, we introduce generalized fractional kinetic equations including extended $k$-Hurwitz-Lerch zeta-matrix functions. By applying the Hadamard fractional integral properties and via the Mellin integral transform, we present the solution of fractional kinetic matrix equations involving families of Hurwitz-Lerch zeta matrix functions. In addition, we consider a number of specific instances of our key results.