In this article, we discuss a conformable fractional Sturm‐Liouville boundary‐value problem. We prove an existence and uniqueness theorem for this equation and formulate a self‐adjoint boundary value problem. We also construct the associated Green function of this problem, and we give the eigenfunction expansions. Finally, we will give some examples.
In this work, we consider singular conformable fractional Sturm-Liouville operators defined by the expressiont 2 y(t) + p(t)y(t), where 0 < t < ∞, ξ ≥ 1 and p(.) is real-valued functions defined on [0, ∞) and satisfy the condition p (.) ∈ L 1 α,loc (0, ∞). 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.
This paper is concerned with the singular dissipative conformable fractional
Sturm-Liouville operators. A completeness theorem for these operators is
proved.
In this study, the opinions of the teachers about the effect of the television serials containing school on the behavior of students were investigated. The data was collected from 233 teachers from Vocational and Anatolia High Schools with the survey technique. As measuring tools; "The School Effects Scale on Student Behavior Scale of Content Series" was used. The collected data were analyzed using SPSS 17.0 statistical software package. Data was analyzed via frequency, t-test, One-Way ANOVA statistical techniques. The obtained data was investigated under five sub-categories; the effect of the school serials on students, the negative effect of students' behavior on teachers and administrators, whether there is difference between the opinions of Anatolia and Vocational High School teachers and their work experiences. In general, according to the result of research, both the Vocational and Anatolian High School teachers' denoted that the serials containing schools, broadcasted a televisions, have negative effect on students' behaviors. When the data was analyzed according to the school type and work experience of teachers, there were not found differences between the opinions of Vocational and Anatolia High School teacher on questionnaire.
In this work, we study the following conformable fractional Sturm-Liouville problemwhere t ∈ [0, ∞), the real-valued functions p and q satisfy the following conditions:p(t) > 0 for all t ∈ [0, ∞). The conformable fractional Sturm-Liouville problem is of the limit-point case if the number of linearly independent α−square integrable solutions of the equation l[y] = λy 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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