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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Some conclusions are presented.
📌 3 Key Takeaways
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Objective & Hypothesis:Öz In the most general case of ω-weights, some normed functional spaces X p ω a, b 1 ≤ p ≤ ∞ , ACn γ,ω[a, b] and a generalization of the fractional integro-differentiation operator are introduced and analyzed.
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Key Findings & Data:The boundedness of the ω-weighted fractional operator over X p ω a, b is proved.
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Conclusion & Impact:Some conclusions are presented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Anahtar Kelimeler ω-weighted fractional derivatives and integrals · functional spaces · representations
Özet
Öz In the most general case of ω-weights, some normed functional spaces X p ω a, b 1 ≤ p ≤ ∞ , ACn γ,ω[a, b] and a generalization of the fractional integro-differentiation operator are introduced and analyzed. The boundedness of the ω-weighted fractional operator over X p ω a, b is proved. Some theorems and lemmas on the properties of the invertions of the mentioned operator and several representations of functions from ACn γ,ω[a, b] are established. A general ω-weighted Caputo fractional derivative of order α is studied over ACn γ,ω[a, b]. Some representations and other properties of this fractional derivative are proved. Some conclusions are presented.
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Cite This Article
AKKURT, A., RESTREPO, J. E., YILDIRIM, H. (2020). Representations and properties of a new family of $\omega$-Caputo fractional derivatives. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 3, 662–675. https://ajindex.com/articles/193178