University of Tabriz Computational Methods for Differential Equations 2345-3982 13 4 2025 10 01 The $(4\alpha-\rho)$ order Sturm-Liouville problem with generalized fractional derivative 1250 1259 19211 10.22034/cmde.2024.60925.2604 EN Mohammad Jafari Department of Science, Payame Noor University, Tehran, Iran. Farhad Dastmalchi Saei Department of Mathematics Faculty of Science Tabriz Branch, Islamic Azad University, Tabriz, Iran. Journal Article 2024 03 15 In this paper, we analyze the generalized fractional derivative with two parameters for fourth-order Sturm-Liouville problems. These  parameters are $\alpha$({\em the fractional order}) and $\rho$ ({\em a real number}). In the following,  we discuss five different forms of Sturm--Liouville problems, which are solved using the $\rho-$Laplace transform. https://cmde.tabrizu.ac.ir/article_19211_7235e1e82b6c4b9c81c017aef21cbd3a.pdf