@article{Nagaraj2026, 
author = {Keerthana Nagaraj and Vivek Devaraj and Abdulah A. Alghamdi and Mohamed M. El-Dessoky and Elsayed Mohamed Elsayed},
title = {Study of complex-valued differential equations with the Hilfer fractional derivative},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {18171-18201},
keywords = {Hilfer fractional derivative, impulsive pantograph equations, complex-valued systems, Banach contraction principle, Krasnoselskii's fixed-point theorem},
url = {https://www.sciopen.com/article/10.3934/math.2026739},
doi = {10.3934/math.2026739},
abstract = {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    ρ  ∈  (  0  ,  1  ) and    ρ  ∈  (  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.}
}