Discontinuous Fractional Sturm-Liouville Problems with Hilfer Derivatives

Abstract

In this paper, we study discontinuous Sturm-Liouville problem with fractional Hilfer derivatives. By defining an operator $A$ in the Hilbert space $L_2[−1, 1],$ this research shows that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the constructed operator. Moreover, the characteristic function is also constructed such that the eigenvalues of the problem are coincide with the zeros of this function.