Universal Journal of Mathematics and Applications (Sep 2023)

On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative

  • Khalid Hilal,
  • Ahmed Kajounı,
  • Samira Zerbib

DOI
https://doi.org/10.32323/ujma.1288015
Journal volume & issue
Vol. 6, no. 3
pp. 122 – 129

Abstract

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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.

Keywords