Ugurlu, Ekin2025-05-112025-05-1120250960-07791873-2887https://doi.org/10.1016/j.chaos.2025.116016https://hdl.handle.net/20.500.12416/9621In this paper, we introduce a singular fractional-order Hamiltonian system with several spectral parameters. Using the inertia indices of the corresponding Hermitian forms we provide a lower bound for the number of linearly independent integrable-square solutions. Moreover, we introduce the Titchmarsh-Weyl function together with an intermediate theorem on the number of the integrable-square solutions. At the end of the paper, we show that 2-sequential and 4-sequential scalar fractional-order differential equations can be embedded into such Hamiltonian systems.eninfo:eu-repo/semantics/closedAccessWeyl TheoryFractional Order DerivativesHamiltonian SystemsInertia IndicesHermitian FormsArticle10.1016/j.chaos.2025.1160162-s2.0-85216591316