文章基本信息

标题：On substantial fractional difference operator
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作者：Syed Sabyel Haider ; Mujeeb ur Rehman
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：1-18
DOI：10.1186/s13662-020-02594-0
出版社：Hindawi Publishing Corporation
摘要：In this article, new definitions of fractional substantial sum and difference operators are introduced. Some properties are established and used to generate a fixed point operator for an arbitrary real order substantial system with conditions involving fractional order difference. We inspect solution existence and Ulam–Hyers–Rassias stability. A property missing in the literature for delta Laplace transform, namely delta exponential shift, is established and used for finding delta Laplace transform for the newly introduced substantial fractional sum and difference.
关键词：Substantial operators;Fractional sum and difference;Delta Laplace transform;Exponential shift;Existence and uniqueness;Ulam–Hyers stability;