Stability analysis for a class of nabla (q; h)-fractional difference equations

Abstract

This paper investigates stability of the nabla (q, h) -fractional difference equations. Asymptotic stability of the special nabla (q, h) -fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunov direct method are proved. Furthermore, we give some new lemmas (including important comparison theorems) related to the nabla (q, h) -fractional difference operators that allow proving the stability of the nabla (q, h) -fractional difference equations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples are given to illustrate these results.

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“…The three most common deletional variants were -SEA , -α 3.7 , and -α 4.2 , which is consistent with previous studies in Fujian province and neighboring provinces (Xu et al, 2004;Zheng et al, 2011;Lin et al, 2014Lin et al, , 2019Dai et al, 2017;Cao et al, 2019;Liu et al, 2019;Chen M. F. et al, 2020). However, the non-deletional variants of α-thalassemia showed a great disparity with other regions (Xu et al, 2004;Zheng et al, 2011;Lin et al, 2014;Liu et al, 2019). Among these variants, 22 cases of rare α-thalassemia were detected, with -THAI /αα and Hkαα/-SEA being the most common.…”

“…In this study, we detected 2,223 chromosomes carrying β-thalassemia gene mutations. The most frequent mutation was IVS-II-654(C > T), which was consistent with several regions in South China (Lin et al, 2014;Dai et al, 2017;Cao et al, 2019;Liu et al, 2019;Chen M. F. et al, 2020). However, the most prevalent β-thalassemia mutation in the nearby provinces of Guangdong and Guangxi is CD41-42(-TCTT) (Xu et al, 2004;Zheng et al, 2011).…”

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