Fundamental solutions of a discontinuous conformable boundary value problem

In this work, information is given about the emergence of fractional calculus and its process until today. After that, some basic properties of the conformable fractional derivative and the Sturm-Liouville problem are given. Then, the discontinuous conformable fractional Sturm-Liouville problem is given and a suitable Hilbert space is defined for the problem. An operator is defined in this space and the given problem is expressed in the form of an operator equation. Finally, the symmetry of the operator and the realness of the eigenvalues are shown.