Jarad, FahdSene, NdolaneAbdeljawad, ThabetMadjidi, Fadila2024-04-292025-09-182024-04-292025-09-182019Abdeljawad, Thabet;...et.al. (2019). "On dynamic systems in the frame of singular function dependent kernel fractional derivatives", Mathematics, Vol.7, No.10.2227-7390https://doi.org/10.3390/math7100946https://hdl.handle.net/20.500.12416/11258Sene, Ndolane/0000-0002-8664-6464; Abdeljawad, Thabet/0000-0002-8889-3768In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.eninfo:eu-repo/semantics/openAccessGeneralized Fractional OperatorsMittag-Leffler BoundMittag-Leffler StabilityArticle10.3390/math71009462-s2.0-85073760984