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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The results are easily verified.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper we study the oscillation of the fractional neutral differential equation $$D^\alpha_t[a(t)D^\alpha(x(t)+p(t)x(\tau(t)))]+q(t)x(\sigma(t))=0,$$ where $D^\alpha_t$ is a modified Riemann-Liouville derivative.
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Key Findings & Data:The obtained results are based on the new comparison theorems, which enable us to reduce the oscillatory problem of 2α-order fractional differential equation to the oscillation of the first order equation.
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Conclusion & Impact:The results are easily verified.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Oscillation · fractional differential equation · modified Riemann-Liouville derivative
Abstract
In this paper we study the oscillation of the fractional neutral differential equation $$D^\alpha_t[a(t)D^\alpha(x(t)+p(t)x(\tau(t)))]+q(t)x(\sigma(t))=0,$$ where $D^\alpha_t$ is a modified Riemann-Liouville derivative. The obtained results are based on the new comparison theorems, which enable us to reduce the oscillatory problem of 2α-order fractional differential equation to the oscillation of the first order equation. The results are easily verified.
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Cite This Article
Zhao, P., Han, Z. L., Wang, Y. Z., Sun, S. (2022). Oscillation theorems for fractional neutral differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 6, 1477–1488. https://ajindex.com/articles/530297