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

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$ pleft( .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.