论文标题
独特性和ulam-hyers-mittag-leffler稳定性结果，用于延迟的分数多物种方程，涉及$φ$ - caputo分数衍生物
Uniqueness and Ulam-Hyers-Mittag-Leffler stability results for the delayed fractional multi-terms differential equation involving the $Φ$--Caputo fractional Derivative
论文作者
论文摘要
本文的主要目的是在$ -Caputo rastional dervivative的背景下建立解决方案的独特性和ULAM-HYERS MITTAG-LEFFLER（UHML）稳定性。为了实现此目的，将广义的拉普拉斯变换方法与方面以及Mittag-Leffler函数（M-LFS）的特性一起用于提供上述问题的解决方案的新表示公式。除此之外，还通过应用众所周知的Banach收缩原则以及$φ$ - 元素的bielecki-type norm，也证明了所考虑问题的解决方案的独特性。虽然$φ$ - 分类的谷仓类型不等式和PICARD操作员（PO）技术与抽象的Gronwall引理相结合，以证明所提出的问题的UHML稳定性结果。最后，提供了一个例子来确保获得的理论结果的有效性。
The principal aim of the present paper is to establish the uniqueness and Ulam-Hyers Mittag-Leffler (UHML) stability of solutions for a new class of multi-terms fractional time-delay differential equations in the context of the $Φ$-Caputo fractional derivative. To achieve this purpose, the generalized Laplace transform method alongside facet with properties of the Mittag-Leffler functions (M-LFs), are utilized to give a new representation formula of the solutions for the aforementioned problem. Besides that, the uniqueness of the solutions of the considered problem is also proved by applying the well-known Banach contraction principle coupled with the $Φ$-fractional Bielecki-type norm. While the $Φ$-fractional Gronwall type inequality and the Picard operator (PO) technique combined with abstract Gronwall lemma are used to prove the UHML stability results for the proposed problem. Lastly, an example is offered to assure the validity of the obtained theoretical results.
