On the Dissipative Extensions of the Conformable Fractional Sturm-Liouville Operator

Authors : Bilender PAŞAOĞLU, Hüseyin TUNA, Yüksel YALÇINKAYA

Pages : 1-5

Doi:10.47000/tjmcs.823775

View : 18 | Download : 2

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :In this work, we consider singular conformable fractional Sturm-Liouville operators defined by the expression \[ \varrho insert ignore into journalissuearticles values(y);=-T_{\alpha }^{2}yinsert ignore into journalissuearticles values(t);+\frac{\xi ^{2}-\frac{1}{4}}{t^{2}}yinsert ignore into journalissuearticles values(t);+% pinsert ignore into journalissuearticles values(t);yinsert ignore into journalissuearticles values(t);,\ \] where $0 < t < \infty ,\ \xi \geq1~$and$\ pinsert ignore into journalissuearticles values(.);\ $is real-valued functions defined on $[0,\infty );$ and satisfy the condition$\ p\leftinsert ignore into journalissuearticles values( .\right); \in L_{\alpha, loc}^{1}insert ignore into journalissuearticles values(0,\infty );$. We construct a space of boundary values for minimal symmetric singular conformable fractional Sturm-Liouville operators in limit-circle case at singular end point. Finally, we give a description of all maximal dissipative, accumulative and self-adjoint extensions of conformable fractional Sturm-Liouville operators with the help of boundary conditions.
Keywords : Dissipative extansions, self adjoint extansion, a boundary value space, boundary condition