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Journals / Universal Journal of Mathematics and Applications / 2023 / Cilt: 6 Sayı: 3

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

Samira ZERBİB
Khalid HİLAL
Ahmed KAJOUNI
Pages
122–129
Publication Date
2023-09-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we give an example to prove our results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:We rely on some arguments to present the mild solution to our problem in terms of an $ \theta $-resolvent family.
💡
Conclusion & Impact:Finally, we give an example to prove our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Atangana-Baleanu-Caputo derivative · Fractional semi-linear differential equation · Krasnoselskii fixed point theorem

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.

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Cite This Article

ZERBİB, S., HİLAL, K., KAJOUNI, A. (2023). On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative. Universal Journal of Mathematics and Applications, Cilt: 6 Sayı: 3, 122–129. https://ajindex.com/articles/965499

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