Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 14 7 2023 07 01 Existence and stability results for a class of nonlinear fractional $q$-integro-differential equation 143 158 7128 10.22075/ijnaa.2022.7128 EN Mohammad Esmael Samei Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, Iran Azam Fathipour Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, Iran Journal Article 2022 03 15 This paper deals with the stability results for the solution of a fractional $q$--integro-differential problem with integral conditions. Using Krasnoselskii's, and Banach's fixed point theorems, we prove the existence and uniqueness of results. Based on the results obtained, conditions are provided that ensure the generalized Ulam stability of the original system on a time scale. The results are illustrated by the examples under the numerical technique. https://ijnaa.semnan.ac.ir/article_7128_46407cc98042b55d22417470dae61194.pdf