河北科技大学学报2026，Vol.47Issue(2)：170-181,12.DOI:10.7535/hbkd.2026yx02006
无穷区间上迭代泛函分数阶q-差分方程的正解
Positive solution of iterative functional fractional q-differential equation on infinite intervals
摘要
Abstract
In order to expand the theory of fractional q-difference equations,the existence of solutions to boundary value problems of a class of iterative functional higher-order fractional q-difference equations with integral boundary conditions on infinite intervals was studied.Firstly,the Green's function of fractional difference equation boundary value problem was calculated and its properties were studied.Secondly,an appropriate Banach space and norm were introduced,and the integral operator was then constructed.Thirdly,the existence theorem of positive solution of the problem was obtained by using monotone iterative technique and upper and lower solution method.Finally,the effectiveness and practicability of the main results were verified by a concrete example.The results show that under certain growth conditions of the nonlinear term g,there exists at least one positive solution to the boundary value problem of iterative functional fractional quantum difference equations on infinite intervals.The research results enrich the solvability theory of fractional q-difference equations,reflect the influence of feedback iterative terms on the existence of solutions,and provide certain theoretical guidance for the application of iterative functional fractional q-difference equations in many fields such as control engineering,biomedicine,population theory,and social economy.关键词
非线性泛函分析/上下解/单调迭代技术/无穷区间/积分边界条件Key words
nonlinear functional analysis/upper and lower solution/monotone iterative technique/infinite intervals/integral boundary conditions分类
数理科学引用本文复制引用
朱月红,禹长龙,李静,王菊芳..无穷区间上迭代泛函分数阶q-差分方程的正解[J].河北科技大学学报,2026,47(2):170-181,12.基金项目
国家重点研发计划项目(2022YFB3806000) （2022YFB3806000）
国家自然科学基金(12272011) （12272011）
