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$\ p\left( .\right) \in L_{\alpha, loc}^{1}(0,\infty )$. 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

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