Aydin, MustafaMahmudov, N. I.2025-05-102025-05-1020241575-54601662-359210.1007/s12346-024-01065-12-s2.0-85195609098https://doi.org/10.1007/s12346-024-01065-1https://hdl.handle.net/20.500.14720/11372Aydin, Mustafa/0000-0003-0132-9636The 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.eninfo:eu-repo/semantics/openAccessFractional Differential SystemPrabhakar Fractional DerivativeGeneralized Peano-Baker SeriesState-Transition MatrixArticle235Q1Q2WOS:001244364400002