In this paper, we establish necessary conditions for the existence of integrable solutions to a general class of initial value problems for nonlinear implicit fractional differential equations (FDEs). The problem is formulated using the Atangana-Baleanu-Caputo derivative with respect to a non-negative, increasing function ψ (i.e. ψ−ABC derivative), along with an argument deviation function, which significantly generalizes the model. By selecting appropriate forms of the deviation function, the proposed problem reduces to well-known classes of FDEs such as pantograph, iterative and implicit FDEs. Furthermore, by taking δ as the identity function, the problem is transformed into a simpler form. The existence of solutions is established using both Banach’s contraction principle and Schauder’s fixed point theorem. Additionally, we demonstrate that the desired solution can be obtained via the Mann iteration process. An illustrative example with exact solution is provided to support the results.