Fractional Sturm-Liouville operators on compact star graphs

被引:0
作者
Mutlu, Gokhan [1 ]
Ugurlu, Ekin [2 ]
机构
[1] Gazi Univ, Fac Sci, Dept Math, TR-06560 Ankara, Turkiye
[2] Cankaya Univ, Fac Arts & Sci, Dept Math, TR-06810 Ankara, Turkiye
关键词
fractional Sturm-Liouville operator; metric graph; transmission condition; fractional-order derivative; star graph; QUANTUM CHAOS;
D O I
10.1515/dema-2024-0069
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 alpha i {\alpha }_{i} of the fractional derivatives on the ith edge lie in ( 0 , 1 ) (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 alpha i -> 1 {\alpha }_{i}\to 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 L 2 {L}<^>{2} space.
引用
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页数:15
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