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Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms

机译:一种具有强制和阻尼条件的一种广义比例分数微分方程的振荡行为

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In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior.
机译:在本文中,我们研究了用矫正和阻尼术语的一种广义比例分数微分方程的解决方案的振荡行为。在Riemann-Liouville和Caputo设置方面建立了几种振荡标准。本文的结果概括了文献中的一些现有定理。实际上,表明,对于参数的特定选择,本文所获得的条件将我们的定理降低到一些已知结果。构建数值示例以证明我们主要定理的有效性。此外,我们展示并说明了不满足我们定理的假设的示例,并且其解决方案展示了非张开行为。

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