Discontinuous Fractional Sturm-Liouville Problems with Hilfer Derivatives (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we study discontinuous Sturm-Liouville problemwith fractional Hilfer derivatives. By defining an operator $A$ in the Hilbertspace $L_2[−1, 1],$ this research shows that the eigenvalues and correspondingeigenfunctions 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 problemare coincide with the zeros of this function.
Keywords: Sturm-Liouville problem; Hilfer derivatives; eigenparameter; fractional boundary conditions; fractional transmission conditions.