University of GuilanJournal of Mathematical Modeling2345-394X11220230701Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method343355668310.22124/jmm.2023.24239.2169ENAlirezaAfaridehDepartment of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, IranFarhadDastmalchi SaeiDepartment of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran0000-0001-9829-2141BehzadNemati SarayDepartment of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran0000-0002-7655-8508Journal Article20230405In this paper, we intend to introduce the Sturm-Liouville fractional problem and solve it using the collocation method based on Chebyshev cardinal polynomials. To this end, we first provide an introduction to the Sturm-Liouville fractional equation. Then the Chebyshev cardinal functions are introduced along with some of their properties and the operational matrices of the derivative, fractional integral, and Caputo fractional derivative are obtained for it. Here, for the first time, we solve the equation using the operational matrix of the fractional derivative without converting it to the corresponding integral equation. In addition to efficiency and accuracy, the proposed method is simple and applicable. The convergence of the method is investigated, and an example is presented to show its accuracy and efficiency.https://jmm.guilan.ac.ir/article_6683_5a49be4f053702e71e18d4c4a590ade9.pdf