Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions

Abstract

In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral fractional Sturm–Liouville problem and discuss the orthogonality of eigenvectors. Finally, we present the numerical results for the considered problem obtained by utilizing the midpoint rectangular rule.

Keywords

• fractional Sturm–Liouville problem
• Neumann boundary conditions
• fractional calculus
• numerical solution
• integral equation