OSCILLATION CRITERIA FOR KERNEL FUNCTION DEPENDENT FRACTIONAL DYNAMIC EQUATIONS

BAHAAELDIN ABDALLA; THABET ABDELJAWAD

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OSCILLATION CRITERIA FOR KERNEL FUNCTION DEPENDENT FRACTIONAL DYNAMIC EQUATIONS

机译：内核功能依赖性分数动态方程的振荡标准

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In this work, we examine the oscillation of a class fractional differ-ential equations in the frame of generalized nonlocal fractional derivatives withfunction dependent kernel type. We present sufficient conditions to prove theoscillation criteria in both of the Riemann-Liouville (RL) and Caputo types.Taking particular cases of the nondecreasing function appearing in the kernelof the treated fractional derivative recovers the oscillation of several provenresults investigated previously in literature. Two examples, where the kernelfunction is quadratic and cubic polynomial, have been given to support thevalidity of the proven results for the RL and Caputo cases, respectively.

机译：在这项工作中，我们检查了类别分数的振荡 - 广义非局部分数衍生物框架中的势方程函数依赖性内核类型。我们提出了足够的条件来证明 riemann-liouville（RL）和Caputo类型的振动标准。特别是在内核中出现的非分泌功能的案例治疗的分数衍生物恢复了几种证明的振荡结果在文献中进行了研究。两个例子，内核功能是二次和立方体多项式，已经给了支持分别对RL和Caputo案件的经过验证结果的有效性。

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来源
《Discrete and Continuous Dynamical Systems,Series S》 |2021年第10期|3337-3349|共13页
作者
BAHAAELDIN ABDALLA; THABET ABDELJAWAD;
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作者单位

Department of Mathematics and General Sciences Prince Sultan UniversityP. O. Box 66833 Riyadh 11586 Saudi Arabia;

Department of Mathematics and General SciencesPrince Sultan UniversityP. O. Box 66833 Riyadh 11586 Saudi ArabiaDepartment of Medical ResearchChina Medical University Taichung 40402 TaiwanDepartment of Computer Science and Information EngineeringAsia University Taichung Taiwan;

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正文语种 eng
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General fractional integrals; derivative of a function with respect to a function; fractional differential equations; oscillation theory; Young's inequality; singular function dependent kernel;

机译：一般分数积分;关于功能的函数的衍生物;分数微分方程;振荡理论;年轻的不平等;奇异函数依赖核;

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OSCILLATION CRITERIA FOR KERNEL FUNCTION DEPENDENT FRACTIONAL DYNAMIC EQUATIONS

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