Nora OuagueniYacine Arioua2023-12-202023-12-202021http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/41766In this paper, we have discussed a special type of nonlinear boundary value problems (BVPs) which involves both the right-sided Caputo-Katugampola (CK) and the left-sided Katugampola fractional deriv atives (FDs). Based on some new techniques and some properties of the Mittag-Le­ er functions, we have introduced a formula of the solution for the aforementioned problem. To study the existence and uniqueness results of the solution for this problem, we have applied some known Öxed point theorems (i.e., Banachís contraction principle, Schauderís Öxed point theorem, nonlinear alternative of Leray-Schauder type and Schaeferís Öxed point theorem). We have also studied the Ulam-Hyers stability of this problem. To illustrate the theoretical results in this work, we have given two examples.Article