Caputo fractional systems with variable coefficients: Existence and stability results via Peano–Baker series
DOI:
https://doi.org/10.66147/lnaa.20264379Abstract
This paper studies linear fractional differential systems with variable coefficients involving the Caputo derivative $(0<\alpha<1)$. The solution framework is formulated in the Banach space $C(\mathscr{I},\mathbb{R}^{n})$, reflecting the regularity of Caputo-type solutions. A state-transition matrix is constructed via the generalized Peano--Baker series and shown to converge uniformly with a Mittag--Leffler bound. Existence and uniqueness results are established for both homogeneous and inhomogeneous problems, with the latter yielding a mixed-kernel representation. Stability of the trivial solution is characterized through Mittag--Leffler estimates and spectral conditions, alongside bounded-input bounded-output stability. Illustrative examples validate the theoretical findings and highlight the analytical framework.
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Copyright (c) 2026 Kavitha Velusamy, Sowmiya Ramasamy, Dumitru Baleanu; Mallika Arjunan Mani (Corresponding Author)
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