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Journals / Results in Nonlinear Analysis / 2026 / 2022 - Cilt 5, Sayı 4

Existence of mild solutions for semilinear $\psi-$Caputo-type fractional evolution equations with nonlocal conditions in Banach spaces

Ali El Mfadel(Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University)0000-0002-2479-1762
Fatima Ezzahra Bourhim(Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University)
M'hamed Elomari(Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University)
Pages
459–472
Publication Date
2022-12-30
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AI Summary & Key Takeaways

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

As application, a nontrivial example is given to illustrate our theoretical results.

📌 3 Key Takeaways

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Objective & Hypothesis:The main crux of this manuscript is to establish the existence of mild solutions for a class of semilinear $\psi-$Caputo-type fractional evolution equations in Banach spaces with non-local conditions.
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Key Findings & Data:The proofs are based on some fixed point theorems, compact semigroup and some basic concepts of $\psi-$fractional analysis.
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Conclusion & Impact:As application, a nontrivial example is given to illustrate our theoretical results.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:$\psi-$fractional integral · $\psi-$Caputo fractional derivative · fixed point

Abstract

The main crux of this manuscript is to establish the existence of mild solutions for a class of semilinear $\psi-$Caputo-type fractional evolution equations in Banach spaces with non-local conditions. The proofs are based on some fixed point theorems, compact semigroup and some basic concepts of $\psi-$fractional analysis. As application, a nontrivial example is given to illustrate our theoretical results.

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Cite This Article

Mfadel, A. E., Bourhim, F. E., Elomari, M. (2022). Existence of mild solutions for semilinear $\psi-$Caputo-type fractional evolution equations with nonlocal conditions in Banach spaces. Results in Nonlinear Analysis, 2022 - Cilt 5, Sayı 4, 459–472. https://doi.org/10.53006/rna.1121916

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