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

Year 2021, Volume: 13 Issue: 1, 19 - 24, 30.06.2021

Yüksel Yalçınkaya , Bilender Paşaoğlu , Hüseyin Tuna

https://doi.org/10.47000/tjmcs.823766

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 $t\in \lbrack 0,\infty ),$ the real-valued functions $p$ and $q$
satisfy the following conditions:
\[
\begin{array}{cc}
(i) & q\in L_{\alpha }^{2}[0,\infty ), \\
(ii) & p\ \text{is\ absolutely\ continuous\ on}\ [0,\infty ), \\
(iii) & p(t)>0\ \ \text{for\ all}\ t\in \lbrack 0,\infty ).%
\end{array}%
\]
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.

Keywords

Sturm-Liouville operator, conformable fractional Sturm-Liouville operator, limit-point case

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