AbstractWe investigate Ulam stability of a general delayed differential equation of a fractional order. We provide formulas showing how to generate the exact solutions of the equation using functions that satisfy it only approximately. Namely, the approximate solution $$\phi $$
ϕ
generates the exact solution as a pointwise limit of the sequence $$\varLambda ^n\phi $$
Λ
n
ϕ
with some integral (possibly, nonlinear) operator $$\varLambda $$
Λ
. We estimate the speed of convergence and the distance between those approximate and exact solutions. Moreover, we provide some exemplary calculations, involving the Chebyshev and Bielecki norms and some semigauges, that could help to obtain reasonable outcomes for such estimations in some particular cases. The main tool is the Diaz–Margolis fixed point alternative.