Title of article :
Computation of eigenvalues of fractional Sturm–Liouville problems
Author/Authors :
Maralani ، E.M. Department of Mathematics - Islamic Azad University, Tabriz Branch , Saei ، F.D. Department of Mathematics - Islamic Azad University, Tabriz Branch , Akbarfam ، A.A.J. University of Tabriz , Ghanbari ، K. Sahand university of Technology
Abstract :
We consider the eigenvalues of the fractional-order Sturm--Liouville equation of the form −cDα0+∘Dα0+y(t)+q(t)y(t)=λy(t),0 α≤1,t∈[0,1], with Dirichlet boundary conditions I1−α0+y(t)|t=0=0andI1−α0+y(t)|t=1=0,where q∈L2(0,1) is a real-valued potential function. The method is used based on a Picard s iterative procedure. We show that the eigenvalues are obtained from the zeros of the Mittag-Leffler function and its derivatives.
Keywords :
Fractional Sturm–Liouville , Fractional calculus , Iterative methods , Eigenvalues
Journal title :
Iranian Journal of Numerical Analysis and Optimization
Journal title :
Iranian Journal of Numerical Analysis and Optimization
