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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t)|_{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
📌 3 Key Takeaways
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Objective & Hypothesis:This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t)|_{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
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Key Findings & Data:This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t)|_{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
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Conclusion & Impact:This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t)|_{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional differential equations · oscillation · asymptotic behavior
Abstract
This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t)|_{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
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Cite This Article
SEEMAB, A., REHMAN, M. U. (2019). On oscillatory and nonoscillatory behavior of solutions for a class of fractional order differential equations. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1182–1194. https://ajindex.com/articles/185547