Abdelhamid, HallouzStamov, GaniSouid, Mohammed SaidStamova, Ivanka2023-09-272023-09-272023-09-20Axioms 12 (9): 895 (2023)https://hdl.handle.net/20.500.12588/2076This paper proposes new existence and uniqueness results for an initial value problem (IVP) of fractional differential equations of nonlinear variable order. Riemann–Liouville-type fractional derivatives are considered in the problem. The new fundamental results achieved in this work are obtained by using the inequalities technique and the fixed point theory. In addition, uniform stability criteria for the solutions are derived. The accomplished results are new and complement the scientific research in the field. A numerical example is composed to show the efficacy and potency of the proposed criteria.Attribution 4.0 United Stateshttps://creativecommons.org/licenses/by/4.0/fractional derivatives and integrals of variable orderfixed point theoreminitial value problemuniform stabilityArticle2023-09-27