On the nonlinear quadratically perturbed fractional differential systems via complex order derivative

Abstract

The aim of this work is to investigate the existence of solutions for a nonlinear quadratically perturbed system involving the $ \psi $-Hilfer fractional derivative of complex order $ \beta \in \mathbb{C} $, where $ \beta= \alpha+ i\gamma $, $ (\alpha, \gamma, \in \mathbb{R}) $ and $ 0< \alpha < 1 $. The existence of solutions is established using Dhage's well-known fixed-point theorem. Finally, an example is provided to illustrate the results of this study.