Approximation and convergence of generalized fractional Sturm-Liouville problem via integral form

Abstract

The aim of this study is to present a numerical algorithm for solving the generalized fractional Sturm-Liouville differential equation. We define the generalized fractional Sturm-Liouville problem (GFSLP) in terms of Caputo fractional derivative with generalized kernel. Firstly, the GFSLP is transformed into an integral form using a weighted Laplace transform. Next, we consider the GFSLP under different cases of boundary conditions. Further, we approximate the generalized fractional integral using Lagrange interpolating polynomial and form an eigenvalue problem for different types of boundary conditions. The bound for the truncation error in the approximation is proved. Finally, the test cases of GFSLPs are considered for numerical simulations of the proposed numerical scheme and examine the theoretical claims. © The Author(s), under exclusive licence to The Forum D’Analystes 2024.