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

Malgorzata Klimek; Mariusz Ciesielski; Tomasz Blaszczyk

doi:10.3390/e24020143

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

Entropy (Basel). 2022 Jan 18;24(2):143. doi: 10.3390/e24020143.

Authors

Malgorzata Klimek¹, Mariusz Ciesielski², Tomasz Blaszczyk¹

Affiliations

¹ Department of Mathematics, Czestochowa University of Technology, al. Armii Krajowej 21, 42-200 Czestochowa, Poland.
² Department of Computer Science, Czestochowa University of Technology, Dabrowskiego 73, 42-200 Czestochowa, Poland.

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: Neumann boundary conditions; fractional Sturm–Liouville problem; fractional calculus; integral equation; numerical solution.