Numerical approximation to Prabhakar fractional Sturm–Liouville problem

In this paper, we treat a numerical scheme for the regular fractional Sturm–Liouville problem containing the Prabhakar fractional derivatives with the mixed boundary conditions. We show that the eigenfunctions corresponding to distinct numerical eigenvalues are orthogonal in the Hilbert spaces. The numerical errors and convergence rates are also investigated. Further, we consider a space-fractional diffusion equation and study the associated fractional Sturm–Liouville problem along with the convergence analysis.