Spectral structure of conformable derivative eigenvalue problems

The thesis consists of six chapters. In the first chapter, a general history of fractional calculations and conformable derivatives are given. Different between classical and conformable derivatives is explained. In the second chapter, fundamental definitions and theorems are given. Fractional power series and conformable Laplace transform are given. In the third chapter, the spectral theory of the conformable Sturm-Liouville problem with normal boundary conditions is analyzed. The fourth and fifth chapters form the original chapters of the thesis. In the fourth chapter, by using the Frobenius method, solutions of the conformable Sturm-Liouville equation having modified Coulomb and hydrogen atom potential are obtained. Additionally, these solutions are analyzed with graphics. In the fifth chapter, the fundamental spectral theory of conformable Sturm-Liouville problem with Coulomb potential is proven. The conformable Lagrange identity theorem is proven. The eigenfunctions corresponding to distinct eigenvalues are α-orthogonal and the representation of the solution are obtained. In the sixth chapter, results obtained from thesis are analyzed in detail. Keywords: Conformable calculus, Sturm-Liouville eigenvalue problem, Spectral theory, Coulomb potential, Singular.