论文标题
研究分数蠕变问题，有多个延迟，以鲍尔茨曼的叠加原则
Study of a Fractional Creep Problem with Multiple Delays in Terms of Boltzmann's Superposition Principle
论文作者
论文摘要
我们研究了具有多个延迟的一类非线性分数微分方程，该方程由粘弹性的Voigt蠕变分数模型表示。我们讨论了两个VOIGT模型，第一种模型是线性的，第二个是非线性的。线性VOIGT模型为我们提供了物理解释，并且与重要结果相关联，因为蠕变功能表征了压力和应变的粘弹性行为。对于VOIGT的非线性模型，我们的理论研究和分析提供了存在和稳定性，其中时间延迟以Boltzmann的叠加原则表示。通过Banach收缩原则，我们证明存在独特的解决方案，并研究了其对初始数据和ULAM稳定性的持续依赖性。结果用一个示例说明了结果。
We study a class of nonlinear fractional differential equations with multiple delays, which is represented by the Voigt creep fractional model of viscoelasticity. We discuss two Voigt models, the first being linear and the second being nonlinear. The linear Voigt model give us the physical interpretation and is associated with important results since the creep function characterizes the viscoelastic behavior of stress and strain. For the nonlinear model of Voigt, our theoretical study and analysis provides existence and stability, where time delays are expressed in terms of Boltzmann's superposition principle. By means of the Banach contraction principle, we prove existence of a unique solution and investigate its continuous dependence upon the initial data as well as Ulam stability. The results are illustrated with an example.
