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.
Atangana-Baleanu-Caputo derivative Fractional semi-linear differential equation Krasnoselskii fixed point theorem Resolvent family
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Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Articles |
Authors | |
Project Number | . |
Publication Date | September 30, 2023 |
Submission Date | April 26, 2023 |
Acceptance Date | September 23, 2023 |
Published in Issue | Year 2023 Volume: 6 Issue: 3 |
Universal Journal of Mathematics and Applications
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