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Left-definite fractional Hamiltonian systems: Titchmarsh-Weyl theory

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  • Uğurlu, Ekin

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.

Suggested Citation

  • Uğurlu, Ekin, 2025. "Left-definite fractional Hamiltonian systems: Titchmarsh-Weyl theory," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007696
    DOI: 10.1016/j.chaos.2025.116756
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    References listed on IDEAS

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    1. M. Abu-Shady & Mohammed K. A. Kaabar, 2021. "A Generalized Definition of the Fractional Derivative with Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, October.
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