Study of complex-valued differential equations with the Hilfer fractional derivative

In this paper, a class of nonlinear impulsive pantograph-type Hilfer complex-valued systems (IPH-CVSes) is investigated. Two cases corresponding to the fractional orders $\rho \in (0,1)$ and $\rho \in (1,2)$ are studied. Explicit solution representations for the considered models are derived. Moreover, existence and uniqueness results are established using Krasnoselskii's fixed-point theorem and the Banach contraction principle. Finally, an application arising from an aerodynamic flow model is provided to demonstrate the applicability of the obtained theoretical results.