- Turkish Journal of Mathematics and Computer Science
- Vol: 13 Issue: 1
- On the Dissipative Extensions of the Conformable Fractional Sturm-Liouville Operator
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 : 11 | Download : 2
Publication Date : 2021-06-30
Article Type : Research
Abstract :In this work, we consider singular conformable fractional Sturm-Liouville operators defined by the expression \[ \varrho (y)=-T_{\alpha }^{2}y(t)+\frac{\xi ^{2}-\frac{1}{4}}{t^{2}}y(t)+% p(t)y(t),\ \] where $0 < t < \infty ,\ \xi \geq1~$and$\ p(.)\ $is real-valued functions defined on $[0,\infty )$ and satisfy the condition$\ p\left( .\right) \in L_{\alpha, loc}^{1}(0,\infty )$. 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