@article { author = {Massah Maralani, Elnaz and Dastmalchi Saei, Farhad and Jodayree Akbarfam, Ali Asghar and Ghanbari, Kazem}, title = {Eigenvalues of fractional Sturm-Liouville problems by successive method}, journal = {Computational Methods for Differential Equations}, volume = {9}, number = {4}, pages = {1163-1175}, year = {2021}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {10.22034/cmde.2020.37867.1671}, abstract = {In this paper, we consider a fractional Sturm-Liouville equation of the form, − cDα 0+ ◦ Dα 0+ y(t) + q(t)y(t) = λy(t), 0 < α < 1, t ∈ [0, 1], with Dirichlet boundary conditions I 1−α 0+ y(t)|t=0 = 0, and I 1−α 0+ y(t)|t=1 = 0, where, the sign ◦ is composition of two operators and q ∈ L2 (0, 1), is a real valued potential function. We use a recursive method based on Picard’s successive method to find the solution of this problem. We prove the method is convergent and show that the eigenvalues are obtained from the zeros of the Mittag-Leffler function and its derivatives.}, keywords = {Fractional Sturm-Liouville,fractional calculus,Sucssesive methods,eigenvalues}, url = {https://cmde.tabrizu.ac.ir/article_10955.html}, eprint = {https://cmde.tabrizu.ac.ir/article_10955_dc410b6dcd91de463c9825edb743a99f.pdf} }