OICC Press Mathematical Analysis and its Contemporary Applications 5 1 2023 01 01 Solving conformable fractional Sturm-Liouville equations using one class of special polynomials and special functions 10.30495/maca.2023.1988807.1070 EN Arsalan Hojat Ansari Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa-0204, South Africa Snježana Maksimović Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka, Bosnia and Herzegovina Journal Article 2023 01 01 The objective of this paper is to solve conformable fractional Sturm-Liouville equations using one class of special polynomials and special functions introduced in [13]. Also, the connection between Mittag-Leffler functions and special polynomials are established and conformable fractional derivatives of certain Mittag-Leffler functions are determined.