Holomorphic and Singular Solutions of <i>q</i>-Difference-Differential Equations of the Gérard-Tahara Type

In 1993, Gérard-Tahara introduced the Fuchs (Gérard-Tahara) type partial differential equation, and they determined the structure of holomorphic and singular solutions provided that the characteristic exponents satisfy some conditions. In this paper the author shows existences of holomorphic and singular solutions of difference-differential equations where the time variable derivative is replaced by q-difference operator.