University of Tabriz Computational Methods for Differential Equations 2345-3982 13 4 2025 10 01 Hyers-Ulam and exponential stabilities of autonomous and non-autonomous difference equations 1125 1134 18375 10.22034/cmde.2024.59702.2544 EN Gul Rahmat Department of Mathematics, Islamia College Peshawar, Pakistan. Afaq Ahmad Department of Mathematics, Islamia College Peshawar, Pakistan. Muhammad Sarwar 1. Department of Mathematics, University of Malakand, Dir Lower, Pakistan.\\ 2. Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia. Kamaleldin Abodayeh Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia. Cemil Tunç School of Engineering and Natural Sciences, Istanbul Medipol University, 34810, Istanbul, Turkey. 0000-0003-2909-8753 Journal Article 2023 12 23  In this manuscript, we studied the Hyers-Ulam and exponential stabilities of autonomous and non-autonomous difference equations of first and second order.  Ultimately, we provide some examples to support our results. Hyer-Ulam Exponential Stability Difference equations https://cmde.tabrizu.ac.ir/article_18375_2e80d047007ef9f3e23b57d339e58eeb.pdf