Fractional Sturm-Liouville Equations: Self-Adjoint Extensions

被引：10

作者：

Tokmagambetov, Niyaz ^{[1
,2
]}

Torebek, Berikbol T. ^{[1
,2
]}

机构：

[1] Al Farabi Kazakh Natl Univ, 71 Al Farabi Ave, Alma Ata 050040, Kazakhstan

[2] Inst Math & Math Modeling, 125 Pushkin Str, Alma Ata 050010, Kazakhstan

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2019年 / 13卷 / 05期

关键词：

Fractional kinetic equation; Caputo derivative; Riemann-Liouville derivative; Green's formula; Self-adjoint problem; Conservation law; The extension theory;

D O I：

10.1007/s11785-018-0828-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this report we study a fractional analogue of Sturm-Liouville equation. A class of self-adjoint fractional Sturm-Liouville operators is described. We give a biological interpretation of the fractional order equation and nonlocal boundary conditions that arise in describing the systems separated by a membrane. In particular, the connection with so called fractional kinetic equations is observed. Also, some spectral properties of the fractional kinetic equations are derived. An application to the anomalous diffusion of particles in a heterogeneous system of the fractional Sturm-Liouville equations is discussed.

引用

页码：2259 / 2267

页数：9

共 12 条

[1]

Ashrafuzzaman M., 2013, Membrane Biophysics

[2] Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary [J].