Ugurlu, Ekin2025-08-052025-08-0520250960-07791873-2887https://doi.org/10.1016/j.chaos.2025.116756https://hdl.handle.net/20.500.12416/10289Hamiltonian systems are useful when formally symmetric boundary value problems generated by ordinary derivatives are considered. However, if the ordinary derivatives are changed by non-integer-order (fractional) derivatives, it is not easy to investigate the corresponding problems. In this paper, we introduce a systematic approach to dealing with fractional boundary value problems by constructing a fractional Hamiltonian system. In particular, we consider a left-definite system, and we construct nested-circles theory (Weyl theory) for this system of equations. Using the Titchmarsh-Weyl function, we prove that at least r-solutions of the 2r-dimensional system of equations should be Dirichlet-integrable on a given interval.eninfo:eu-repo/semantics/closedAccessHamiltonian SystemsLeft-DefinitenessFractional DerivativesWeyl TheoryArticle10.1016/j.chaos.2025.1167562-s2.0-105009289238