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

Samira Zerbib; Khalid Hilal; Ahmed Kajouni

doi:10.5269/bspm.75731

Samira Zerbib Laboratory of Applied Mathematic & Scientific Calculus, Sultan Moulay Slimane University, Beni Mellal
Khalid Hilal Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco https://orcid.org/0000-0002-0806-2623
Ahmed Kajouni Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco https://orcid.org/0000-0001-8484-6107

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.

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