Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions
Małgorzata Klimek, Mariusz Ciesielski, Tomasz Błaszczyk
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.
Topics & Concepts
Sturm–Liouville theoryMathematicsDiscretizationNeumann boundary conditionNeumann seriesFractional calculusMathematical analysisOrthogonalityBoundary value problemEigenvalues and eigenvectorsEigenfunctionHomogeneousGeometryCombinatoricsQuantum mechanicsPhysicsFractional Differential Equations SolutionsDifferential Equations and Boundary ProblemsNumerical methods in engineering