On Hilfer fractional difference operator

被引：0
作者：
Syed Sabyel Haider
Mujeeb ur Rehman
Thabet Abdeljawad
机构：
[1] National University of Sciences and Technology,School of Natural Sciences
[2] Prince Sultan University,Department of Mathematics and General Sciences
[3] China Medical University,Department of Medical Research
[4] Asia University,Department of Computer Science and Information Engineering
来源：
Advances in Difference Equations | / 2020卷
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; 39A70; 39A12; 34A12;
D O I：
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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.
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