Fractional Hamiltonian systems: Nested ellipsoids

Ekin Uğurlu

Chaos, Solitons & Fractals, 2025, vol. 192, issue C

Abstract: In 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.

Keywords: Weyl theory; Fractional order derivatives; Hamiltonian systems; Inertia indices; Hermitian forms (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000293

DOI: 10.1016/j.chaos.2025.116016

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