  The notion of moment differentiation is extended to the set of generalized
multisums of formal power series via an appropriate integral representation and
accurate estimates of the moment derivatives. The main result is applied to
characterize generalized multisummability of the formal solution to a family of
singularly perturbed moment differential equations in the complex domain,
broadening widely the range of singularly perturbed functional equations to be
considered in practice, such as singularly perturbed differential equations and
singularly perturbed fractional differential equations.

Classical Analysis and ODEs;Complex Variables