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Dergiler / 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
Sayfa
122–129
Yayın Tarihi
2023-09-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we give an example to prove our results.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
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Temel Bulgular & Veri:We rely on some arguments to present the mild solution to our problem in terms of an $ \theta $-resolvent family.
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Sonuç & Katkı:Finally, we give an example to prove our results.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (14)

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