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

中文翻译：

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核函数相关分数阶动力学方程的振荡准则

在这项工作中，我们研究了具有函数相关核类型的广义非局部分数阶导数框架中一类分数阶微分方程的振荡。我们提出了充分的条件来证明 Riemann-Liouville (RL) 和 Caputo 类型的振荡标准。以处理后的分数阶导数的核中出现的非递减函数的特殊情况为例，可以恢复先前在文献中研究的几个已证明结果的振荡。给出了核函数为二次多项式和三次多项式的两个示例，分别支持 RL 和 Caputo 案例的证明结果的有效性。