Fractional Sturm-Liouville operators on compact star graphs

• Autorzy: Mutlu Gökhan , Uğurlu Ekin

Identyfikatory

DOI

10.1515/dema-2024-0069

• Języki publikacji: EN

Abstrakty

EN

In this article, we examine two problems: a fractional Sturm-Liouville boundary value problem on a compact star graph and a fractional Sturm-Liouville transmission problem on a compact metric graph, where the orders αi of the fractional derivatives on the ith edge lie in (0,1). Our main objective is to introduce quantum graph Hamiltonians incorporating fractional-order derivatives. To this end, we construct a fractional Sturm-Liouville operator on a compact star graph. We impose boundary conditions that reduce to well-known Neumann-Kirchhoff conditions and separated conditions at the central vertex and pendant vertices, respectively, when αi→1. We show that the corresponding operator is self-adjoint. Moreover, we investigate a discontinuous boundary value problem involving a fractional Sturm-Liouville operator on a compact metric graph containing a common edge between the central vertices of two star graphs. We construct a new Hilbert space to show that the operator corresponding to this fractional-order transmission problem is self-adjoint. Furthermore, we explain the relations between the self-adjointness of the corresponding operator in the new Hilbert space and in the classical L2 space.

Słowa kluczowe

EN

fractional Sturm-Liouville operator; metric graph; transmission condition; fractional-order derivative; star graph

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240069
• Opis fizyczny: Bibliogr. 43 poz., rys.

Twórcy

autor

Mutlu Gökhan

• Department of Mathematics, Faculty of Science, Gazi University, 06560, Ankara, Turkey

autor

Uğurlu Ekin

• Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, 06810, Ankara, Turkey

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).