Limit-point Classification for Singular Conformable Fractional Sturm-Liouville Operators

Abstract

In this work, we study the following conformable fractional Sturm--Liouville problem[l[y]=-T_{alpha }(p(t)T_{alpha }y(t))+q(t)y(t),] where $tin lbrack 0,infty ),$ the real-valued functions $p$ and $q$ satisfy the following conditions:[begin{array}{cc} (i) & qin L_{alpha }^{2}[0,infty ), (ii) & p text{is absolutely continuous on} [0,infty ), (iii) & p(t)>0 text{for all} tin lbrack 0,infty ).% end{array}%] The conformable fractional Sturm--Liouville problem$ $is of the limit-point case if the number of linearly independent $alpha -$square integrable solutions of the equation$ l[y]=lambda y $is less than 2. We give a criterion for the limit point classification of conformable fractional Sturm-Liouville operators in singular case.