Abstract

In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial condition. We acquire some conditions for existence, uniqueness, Ulam–Hyers, and Ulam–Hyers–Rassias stability. Modified Gronwall’s inequality is presented for discrete calculus with the delta difference operator.

中文翻译：

---

关于Hilfer分数差分算子

摘要

本文介绍了分数希尔弗差分算子的新定义。开发了基于定义的属性，并将其用于构造具有初始条件的分数阶Hilfer差分方程的不动点算子。我们为生存，唯一性，Ulam-Hyers和Ulam-Hyers-Rassias稳定性获取了一些条件。利用增量差算子，针对离散演算提出了修正的Gronwall不等式。