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Left-definite fractional Hamiltonian systems: Integrable-square solutions

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  • Uğurlu, Ekin

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.

Suggested Citation

  • Uğurlu, Ekin, 2026. "Left-definite fractional Hamiltonian systems: Integrable-square solutions," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014043
    DOI: 10.1016/j.chaos.2025.117391
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    References listed on IDEAS

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    1. Virginia Kiryakova, 2020. "Unified Approach to Fractional Calculus Images of Special Functions—A Survey," Mathematics, MDPI, vol. 8(12), pages 1-35, December.
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