@article{article_823775, title={On the Dissipative Extensions of the Conformable Fractional Sturm-Liouville Operator}, journal={Turkish Journal of Mathematics and Computer Science}, volume={13}, pages={1–5}, year={2021}, DOI={10.47000/tjmcs.823775}, author={Paşaoğlu, Bilender and Tuna, Hüseyin and Yalçınkaya, Yüksel}, keywords={Dissipative extansions, self adjoint extansion, a boundary value space, boundary condition}, 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.}, number={1}, publisher={Matematikçiler Derneği}