Left-definite fractional Hamiltonian systems: Integrable-square solutions

Ekin Uğurlu

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: In this paper, we introduce a 2r−dimensional fractional Hamiltonian system in which the weight matrix has an arbitrary sign on the given singular interval. Using the matrix analysis we construct ellipsoids. Indeed, using a transformation we construct regular selfadjoint boundary conditions, and we define the characteristic matrix subject to the regular boundary value problem. We show that the sets consisting of the characteristic matrices subject to regular boundary value problems are nested and nonempty. Then we introduce a lower bound for the number of Dirichlet integrable solutions. Moreover we share some properties of the Titchmarsh–Weyl matrix for the left-definite case.

Keywords: Hamiltonian systems; Weyl theory; Fractional calculus; Left-definite equations (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014043

DOI: 10.1016/j.chaos.2025.117391

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