AL-Towailb, Maryam A.2022-04-082022-04-082017-03-28AL-Towailb, M. A. (2017). A q-fractional approach to the regular Sturm-Liouville problems. <i>Electronic Journal of Differential Equations, 2017</i>(88), pp. 1-13.1072-6691https://hdl.handle.net/10877/15620In this article, we study the regular q-fractional Sturm-Liouville problems that include the right-sided Caputo q-fractional derivative and the left-sided Riemann-Liouville q-fractional derivative of the same order, α ∈ (0, 1). We prove properties of the eigenvalues and the eigenfunctions in a certain Hilbert space. We use a fixed point theorem for proving the existence and uniqueness of the eigenfunctions. We also present an example involving little q-Legendre polynomials.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalBoundary value problemsEigenvalues and eigenfunctionsLeft and right sided Riemann-LiouvilleCaputo q-fractional derivativesArticle