Left-definite fractional Hamiltonian systems: Titchmarsh-Weyl theory

Ekin Uğurlu

Chaos, Solitons & Fractals, 2025, vol. 199, issue P2

Abstract: Hamiltonian 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.

Keywords: Hamiltonian systems; Left-definiteness; Fractional derivatives; Weyl theory (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007696

DOI: 10.1016/j.chaos.2025.116756

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