A Study on Linear Prabhakar Fractional Systems with Variable Coefficients

The focus of this paper is on addressing the initial value problem related to linear systems of fractional differential equations characterized by variable coefficients, incorporating Prabhakar fractional derivatives of Riemann–Liouville and Caputo types. Utilizing the generalized Peano–Baker series technique, the state-transition matrix is acquired. The paper presents closed form solutions for both homogeneous and inhomogeneous cases, substantiated by illustrative examples.