Fundamental spectral theory of singular sturm-liouville operators with local derivative and their applications

In this study, some substantial data for the Sturm-Liouville problem with separated boundary conditions of newly defined M-derivative which contains Mittag-Leffler functions has been examined. The historical background of the work is mentioned in the first part which consists five chapters. In the second part, the basic definitions and theorems of the study are given. In the third part, the spectral data of the Sturm-Liouville boundary value problem on a finite interval is shown in detail. In the fourth part, the M-derivative singular Sturm-Liouville has been studied. Finally in the last chapter, we examine scientific results and interpretation of the related results given with graphs.