@article{article_1288015, title={On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative}, journal={Universal Journal of Mathematics and Applications}, volume={6}, pages={122–129}, year={2023}, DOI={10.32323/ujma.1288015}, author={Zerbib, Samira and Hilal, Khalid and Kajounı, Ahmed}, keywords={Atangana-Baleanu-Caputo derivative, Fractional semi-linear differential equation, Krasnoselskii fixed point theorem, Resolvent family}, abstract={This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < \theta < 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ \theta $-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii’s fixed point theorem. Finally, we give an example to prove our results.}, number={3}, publisher={Emrah Evren KARA}, organization={.}