论文标题
具有非局部积分边界值条件的Hilfer分数Langevin方程的耦合系统的存在和稳定性结果
Existence and stability results for a coupled system of Hilfer fractional Langevin equation with non local integral boundary value conditions
论文作者
论文摘要
本文介绍了具有非局部积分边界价值条件的Hilfer分数Langevin方程的耦合系统的解决方案的存在和唯一性。这项工作的新颖性是，它比基于Caputo和Riemann-Liouville的衍生产品的作品更一般，因为当$β= 0 $时，我们会发现Riemann-Liouville分数衍生物，当$β= 1 $时，我们找到了Caputo分数衍生物。最初，我们提供了一些定义和概念，这些定义和概念将在整个工作中使用，此后我们将通过采用固定点定理来确定存在和唯一性结果。最终，我们研究了各种稳定性，例如Ulam-hyers稳定性，广义ULAM-HYERS稳定性。
This paper deals with the existence and uniqueness of solution for a coupled system of Hilfer fractional Langevin equation with non local integral boundary value conditions. The novelty of this work is that it is more general than the works based on the derivative of Caputo and Riemann-Liouville, because when $β=0$ we find the Riemann-Liouville fractional derivative and when $β=1$ we find the Caputo fractional derivative. Initially, we give some definitions and notions that will be used throughout the work, after that we will establish the existence and uniqueness results by employing the fixed point theorems. Finaly, we investigate different kinds of stability such as Ulam-Hyers stability, generalized Ulam-Hyers stability.
