On the numerical solution of fractional Sturm–Liouville problems

Abstract

The differential equation of Sturm-Liouville problems is generalized into fractional form by replacing the first-order derivative by a fractional derivative of order α, 0<α≤1. We showed briefly that this class of eigenvalue could be very promising to the solution of linear fractional partial differential equations. The homotopy perturbation method is considered for computing the eigenelements of the present problem. Based on our simulations some theoretical conjectures are reported.

Keywords:

• Sturm–Liouville problems
• fractional Sturm–Liouville problems
• fractional calculus
• eigenvalues and eigenfunctions
• homotopy perturbation method

2000 AMS Subject Classifications :

• 26A33
• 74G15