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

Authors : Yüksel YALÇINKAYA, Bilender PAŞAOĞLU, Hüseyin TUNA

Pages : 19-24

Doi:10.47000/tjmcs.823766

View : 48 | Download : 7

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :In this work, we study the following conformable fractional Sturm--Liouville problem \[ l[y]=-T_{\alpha }insert ignore into journalissuearticles values(pinsert ignore into journalissuearticles values(t);T_{\alpha }yinsert ignore into journalissuearticles values(t););+qinsert ignore into journalissuearticles values(t);yinsert ignore into journalissuearticles values(t);, \] where $t\in \lbrack 0,\infty );,$ the real-valued functions $p$ and $q$ satisfy the following conditions: \[ \begin{array}{cc} insert ignore into journalissuearticles values(i); & q\in L_{\alpha }^{2}[0,\infty );, \\ insert ignore into journalissuearticles values(ii); & p\ \text{is\ absolutely\ continuous\ on}\ [0,\infty );, \\ insert ignore into journalissuearticles values(iii); & pinsert ignore into journalissuearticles values(t);>0\ \ \text{for\ all}\ t\in \lbrack 0,\infty );.% \end{array}% \] 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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