文章基本信息

标题：On Hilfer fractional difference operator
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作者：Syed Sabyel Haider ; Mujeeb ur Rehman ; Thabet Abdeljawad 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-20
DOI：10.1186/s13662-020-02576-2
出版社：Hindawi Publishing Corporation
摘要：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.
关键词：Hilfer fractional difference ; Discrete Mittag-Leffler functions ; Delta Laplace transform ; Gronwall’s inequality ; Existence and uniqueness ; Ulam stability of initial value problem ;