Turkish Journal of Mathematics and Computer Science

Yazarlar: Bilender PAŞAOĞLU ALLAHVERDİEV, Yüksel YALÇINKAYA, Hüseyin TUNA

Konular:Matematik

DOI:10.47000/tjmcs.823766

Anahtar Kelimeler:Sturm-Liouville operator,Conformable fractional Sturm-Liouville operator,Limit-point case

Özet: 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.

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