Estimates of formal solutions for some generalized moment partial differential equations

Using increasing sequences of real numbers, we generalize the idea formal moment differentiation first introduced by W. Balser and M. Yoshino. Slight departure from concept Gevrey enables us to include a wide variety operators in our study. Basing approach on tools such as Newton polygon divergent norms, obtain estimates for solutions certain families generalized linear partial differential equations with constant time variable coefficients.